I wouldn’t think so. More mass (although very mimimal in this case) will hurt braking performance in general rather than help. When it comes to adding weight over the rear wheels specifically, the rear brakes do considerably less braking than fronts – brakes are pretty heavily biased toward the front in automobiles, as they carry less load and the weight transfer under braking goes to the front wheels. Putting weight in the bed of a RWD truck is one thing, but in the trunk of a FWD car, I don’t think you’ll see any advantages, be it in traction OR braking.
I agree with most of the others here suggesting that winter tires might normally be appropriate, but in your case for just the move they are probably an unnecessary expense and overkill if you don’t plan to spend much time in these conditions in the long run.
Ultimately things like ABS or AWD or putting weight over an axle or using kitty litter for traction are all side effects of simply not having appropriate traction, and you should not rely on any of them if your tires are not achieving traction on snow and ice.
California does post when chains are required in the mountainous regions, but I think they may be a bit overkill and are definitely a pain to deal with.
My suggestion: if you don’t want the hassle of carrying and coping with heavy chains, and don’t want the expense of purchasing a dedicated set of cold weather tires, there is another option known as textile snow chains which really are more accurately described as “tire socks”. They fit around the tire in a similar fashion to chains, but look like little booties and are made of a textured fabric that grips snow and ice at low temperatures. There’s one company called ISSE that makes a variety of them. They are more expensive than chains, but also a lot easier to deal with, both in terms of mounting and storage, because they are not anywhere near as bulky or heavy, and don’t get tangled up in themselves. They even make a “hybrid” tire sock that has the best of both worlds: the ease of a sock design with chain link studs in it for even more grip. Granted, they probably aren’t as durable as chains in the long run and may wear out faster if you take them over really rough terrain, but they are light as a feather so you can pretty much keep them in the car at all times if you want.
I would say if you plan to spend more than a brief amount of time in snowy conditions to go for a dedicated set of winter tires, but if it’s only a temporary concern then these tire socks are probably the best bang for the buck in terms of practicality and effectiveness.
I don’t have a cite, and I might very well be wrong. Happens so much it doesn’t even phase me anymore. But every time I drive on 80 over Donner, there are signs that say “Must Carry Chains”.
But the signs are blue, so not sure what that means in California.
Funny story: The day I bought my BMW 740 in the Bay Area, it was storming like a mother! Got up to around Norden and there were chain controls. I got up to the guy, rolled down my window, shouted, “X-Drive!” and motored right on by him! What’s he gonna do? Chase me?
Made it home fine.
To the OP: With the winter he are having so far, you can move in a convertible or motorcycle. Not a whole lot of snow to worry about. Lets hope that changes soon…
You’ve reminded me of another point - you need to get your car winterized if you’re moving from a place that stays warm to one that gets an actual winter. That should include having the proper antifreeze in your radiator so your block doesn’t freeze solid. I don’t know if you’ll need a block heater or not - does it get really cold where you’re moving to, OP?
A humourous aside - I was an adult before I learned that cars don’t come with block heaters installed. I just assumed that they came from the factory like that, because I’d never seen a car without a cord sticking out from under the hood. 
One other point that people should know about gasoline.
If you buy some gasoline with the idea of saving it and using it later, you should know that gasonline only keeps good for about a year. If you try to use some gasoline after one year, it will not be good any longer than that.
I don’t know why. But it can be very disappointing - even dangerous.
Not more dangerous BOOM, though.
My advice for your move would be to look at the forecast for Mt. Shasta. Hint: it’s in the 50s with a 0% chance for precipitation for the next 10 days. I think you’ll be fine with the Uhaul.
The thing about snow tires is that they are not simply for when there is snow on the road. In reality, they are made of a different formulation of rubber, which works better on roads when it is cold - snow or not.
In short, the main question is not whether you get heaps of snow (although that is obviously important), but whether it gets cold.
That said, driving all-seasons in the cold is perfectly possible - it is just less safe. If you are regularly driving in winter weather, snow tires are a good investment.
My parents told me to have my car winterized when I moved to Massachusetts (from Florida). So I took it to the local car guy and said, “I just moved from Florida, I think I need to have my car ‘winterized’?”
And the grizzled Boston-area mechanic looked at me like I’d grown another head.
After which, he explained that in modern cars, they really just change the oil and antifreeze and check the air in the tires. There’s not much else “winterizing” that needs to happen in this area unless you put on snow tires (I don’t). (About the heater block, no idea…don’t need them here in my area of New England.)
I do swap out my windshield wipers to some “winter” ones that clear snow and slush better, but that’s a personal preference.
Yeah. “Winterize” has gone the way of carburettors and single-weight oil. There is nothing left to winterize. Even anti-freeze doesn’t count, since it has to be run year round.
Asking to have a car winterized gives the mechanic permission to replace the fazzaltron, grind the zikaholky, stick a target on your back and charge you $2,800.
Doesn’t Boston get cold enough to require lower temperature oil and antifreeze? Why would a car from Florida have cold-rated fluids in it? I feel like I’m missing something here. 
The manufacturer of my car, for example, specifies 5W-30 engine oil, whether in Winnipeg in January when it’s 40 below or in Death Valley in July. The same car sold in Boston or Florida would specify the same engine oil (and anti-freeze).
Anti-freeze is a chemical soup and must be in modern cars summer and winter because of its anti-rust properties, lubrication properties (the “water” pump for one) and its high boiling point.
Installing a block heater and snow tires were never considered part of “winterizing” a car. It referred to fluids and sometimes grease.
Short answer is no. If you’re up in northern Maine or far upstate NY it may pay to use a different oil or different concentration of antifreeze, but beyond that there’s no reason. Oil and antifreeze in the default configurations now cover essentially all operating conditions.
To get major benefit from a block heater you need sustained temps below -10 F or so. In most of New England you rarely get those temps for multiple days on end, and certainly not in any major cities. In the far north of New England, NY, the upper midwest, the Rockies, and big swaths of Canada it would certainly be worthwhile.
Never used a block heater in Toronto for the past decade; never had a problem. Modern cars are much tougher than cars used to be.
To my mind, really the only concession to the weather (at least as far as Toronto & southern Ontario weather goes) is to get winter tires. Those do make a noticable difference in handling, and so safety.
The last car I had with a block heater was an 89 Dodge Colt. I never actually used it and the car always started like a dream even during Winnipeg winters. I think the last time I actually used a block heater was in my old 76 Chevette when I lived in Cold Lake, AB in the late 80s.
A car’s starting isn’t the only issue. A block heater ensures that the oil isn’t too thick to reach everywhere it’s supposed to on startup.
The car may start in severe cold, but over time there’ll be accelerated wear. You might hear it happening with valve ticking or louder metal-on-metal clatter caused by a lack of lubrication and that disappears as the engine warms.
Is this still a serious concern with newish cars and synthetic oils in ordinary winter temps? I honestly do not know.
Also, the rate of wear, and the temp at which wear can be expected. If wear happens only when it is super-cold, it may not happen enough to make a big difference to engine life.
In any event, I can’t picture myself remembering to plug the car in three hours before going for a drive, unless it was necessary to start the car. I’m lazy. 
Ah, that must be the piece of the puzzle I was missing. I always take my car in for its tune-up/oil change in fall, and they always test my antifreeze to make sure it’s good to go for our low temperatures here (it always is).
As for remembering to plug in the car, you can’t start your car once or twice on the coldest morning of the year because you didn’t bother to plug in, and you start remembering (or get a timer). 
Well, yes, that would certainly do it! Hence my point that, in merely “Toronto-level cold”, and with a newish car, it hasn’t proved ‘necessary’ (where ‘necessary’ is defined by ‘car will not start’).
In short - lazy me will not remember to plug in merely to save engine wear (unless evidence is produced that this is really serious), but would be motivated to plug in if the damn thing won’t start otherwise. Which, in my ville, hasn’t proved necessary.
It’s still very much an issue on the Canadian prairies anyway, where an ordinary winter means crazy cold.
As I type this (all temps Farenheit) it’s –4 and snowing. Yesterday the temp warmed up from -23 in the morning to –10 or so in the afternoon. Temps of –35 and colder (without the wind-chill factor), especially at night, are far too common. (Wind chills don’t affect cars.)
With any of those temperatures and the block heater hasn’t been plugged in, or not plugged in long enough, (four hours seems to be optimum with this car — years ago I had a V8 with two block heaters), the starter turns much more — way more — slowly than when the car was plugged in, and for many more turns. And it takes much longer for the temp-guage needle to crawl off dead cold — as long as nearly a kilometre, or more than half a mile.
(I don’t drive my car faster than idle speed until the temp needle moves — up and down alleys/back lanes. At those temperatures, road speeds with thick oil is engine torture and the auto transmission needs warming up, too.)
In those same temperatures when the car’s been plugged in, at idle speed the temp guage moves off dead cold about 15 closely spaced houses down the back lane.
So by plugging in the block hearter, the starts are easier on the battery, the oil goes to where it’s needed more quickly (and no valve noise and other clatter — the car has about 97,000 miles on it, translated from kilometres — and the cabin heater works much faster.
This is the first car in which I’ve used fully synthetic oil since I bought the thing, because even if the synthetic stuff has the same viscosity as “dino,” or mineral, oil, it pours easier and faster than dino when you need a knife to cut the atmosphere (I’ve experimented pouring both). Even with fully synthetic, the difference between plugging in the car and not plugging it in is dramatic.
For more than you (or probably anyone) ever cares to know about engine oil,
click here. But don’t say I didn’t warn you.
Edit: Sorry. I missed you’re in or near Toronto, hence the Fahrenheit/miles stuff.