What does this entail usually?
What should I do to my car (or have done) before winter hits?
Change the oil to a lighter weight if you live in cold country (5w-20). Check your antifreeze level to make sure it’s good down to the coldest expected temperatures. If you have a relatively flat windshield, buy winter wiper blades for snow (they don’t work well on curved glass). Put a good coat of wax on the car. Check your battery electrolytes, if needed. If you don’t have a garage, consider a block heater for the car.
I’m not from a particularly cold climate, but here are the general steps:
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Check the concentration of antifreeze/water in the cooling system. You don’t want this to freeze! Most of the testers (esp. the Prestone one) have a temperature scale telling you how low the tested coolant will protect to. Make sure that your coolant will ride out the coldest expected temperatures with a little bit of room.
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Make sure your windshield washer reservoir is filled with antifreeze.
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Make sure you have a good multigrade oil sufficient for your expected winter temperatures. Your owner’s manual should specify weights of oil for different temperatures. In my case, 10w-30 is good above 0, while 5w-30 is good at any temperature. If your car is in a particularly cold area, consider using synthetic oil such as Mobil 1. Synthetic oil has much better low temperature performance than conventional mineral oil.
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I don’t know much about this, but make sure your tires are appropriate to the conditions. Someone from up north can tell you more about that- whether snow tires are needed, etc…
That’s about all I can think up now.
Just noted that you live near Chicago. Probably lots of ice. I’d throw a couple of bags of sand in the trunk, especially if you own a rear-wheel drive vehicle.
Most tires today are all-weather, so you may not need to change them out for winter.
Would a radiator flush be appropriate?
How about a transmission fluid flush?
I need to go in to get my belts replaced anyway and was thinking about what other things I could get done.
Much of this is either common sense, or regular preventive maintenance.
Tires: Ensure proper inflation, and tread depth. Don’t forget the spare. If you have chains or cable chains, put them in the trunk, after inspecting the rubber tensioners regarding rot.
Windshield washer/wiper: Replace blades if they are streaky, and fill washer reservoir.
Coolant: Check to make sure it is topped off, and evaluate freeze point. If coolant is old or dirty, have it cleaned/flushed/replaced.
Rubber door seals: Treat them with a proper lube to preclude sticking and tearing during freezing weather.
Lock cylinders: Treat with a spray lubricant which displaces moisture. Wipe off the key after working the lubricant so you don’t stain clothes.
Lighting: Check all bulbs to make sure they are working.
Battery: How old is it? If approaching 5 years, have it load tested, and the alternator waveform analyzed.
Belts: Check for cracking and glazing. Replace as needed.
Exhaust system: Ensure it to be free of leaks which could be poisonous were you stopped for a lengthy period in traffic.
Misc: A survival blanket, a cigarette charger for your cell phone, and some power bars (MREs) can’t hurt.
This may be too much or not enough based on your climate.
I do own a rear-wheel drive vehicle and always do this. It’s practically a necessity. Also It gives you something to throw under the wheels if you’re not getting traction.
This one wouldn’t have occurred to me. Is silicone oil good for this?
That should work. I use a dry-release lubricant and wipe the seals, as well as the mating portion of the door jambs.
Suppose I figure I need to increase the percentage of antifreeze in my cooling system, but that my cooling system already seems to be ‘full’. I can’t find any sort of tap or ‘drain’ that would allow me to run off some of the existing coolant to create room to add the antifreeze. What to do?
Ditto with the windshield (or windscreen, as we say here in Brit-land) washer reservoir. Suppose it’s full or full-ish and there’s no apparent way to drain it to make some room. Solution?
If the system is already full, you’ll need to look at the base of the radiator for a stop-cock or drain to allow removal of some fluid. Be careful, as the glycol-based fluid is tempting to dogs and cats, but is lethal if ingested.
If the windshield washer reservoir is full-did you fill it with undiluted fluid during summer months? In the US, the blue juice is good against freezing when used full strength. I dilute during the summer-using a 50-50 mix, and try to run it down when fall arrives, refilling with full strength.
In addition to all of the above good advice, go find what box in the garage you shoved the snow/ice scraper in last spring, dig it out, and put it in your trunk or inside your car (wherever you typically keep it).
All season tires are a compromise between good weather tires and bad weather tires. Since they are a compromise, they tend to pretty much suck (IMHO). If you buy tires specifically for rain or snow or whatever the weather tends to be in your area this time of year, they will give you a lot better traction than the all season tires. Having 2 sets of tires gets to be a bit pricey though, and isn’t practical if you live in an apartment and don’t have room to store the set you aren’t using. If you are in a really snowy area (did someone say the OP is near Chicago?) they are worth the investment (IMHO). You’ll want to get the snow tires back off of the car as soon as the good weather comes though, because they tend to wear out a lot faster and get much worse mileage on good clear roads than regular tires.
I personally have an even much more expensive solution. I have a good weather car and a bad weather car. Actually the bad weather car is a 4x4 truck. I don’t get stuck in the snow. 
Actually while most folks don’t have 6 cars like I do (in a house where only 2 people drive, which makes it even worse) but I know a lot of folks in areas like Chicago and New York who have bad weather beaters and good weather good cars. They keep the good car in the garage all winter and let the salt and road crap eat away at the cheap beater all winter.
You might also want to pick up a can of that stuff that you can spray onto your door locks and de-ice them. Keep it in the house. It won’t do much good if it’s in the car and you can’t get into the car because the locks froze up. 
Also you might want to keep a set of jumper cables in the trunk.
My winter car kit, which sits in my trunk from October - April (I live in Minnesota):
- shovel
- bucket (3-gallon plasitc ice cream tubs work very well) of sand
- winter overalls (snowsuit), hat, gloves.
- a couple of Snickers bars
- butane cigarette lighter and a candle or two
- Ice scraper/brush (these generally go in the passenger compartment, under the driver’s seat)
Good points have already been raised about the radiator coolant, washer fluid, oil, and snow tires. I also generally try refill my gas tank when it gets below 1/2 full, as this helps keep mositure condensation (water) out of the tank and if you’re skid off the road, you’ll have some fuel to run the engine and the heater while waiting for help.
Hmm, I live in the frozen north, and I don’t do nuthin’ to “winterize” my vehicle.
OK, not quite true. I do dig out the scraper and put it in the back seat.
Radiator flush should not be needed annually - perhaps once in 3-4 years. It probably has more to do with being ready for hot weather than for winter.
Transmission fluid flush is not specific to winter preparation. I do this about once per 25k miles; most people seem happy to wait much longer. If you go to one of those quick-lube joints, don’t let them talk you into not changing the transmission filter, and don’t accept the spiel about how one type of fluid (the one they happen to have on hand) is good for all makes and models.
Chains, shovel, traction mats, winch/tow straps/ropes/pulleys, jumper cables, wrenches/screwdrivers/plyers/large hammer, flares, first aid/survival kit, candle/matches, winter sleeping bag, parka, winter boots, insulated gloves.
and brush/scraper.
The concept of “winterizing” is a holdover from years gone by. There was a time (long ago) when engine coolant was changed seasonally, and later when a coolant flush and fill was recommended annually. Nowadays I think it’s more appropriate to think in terms of a “winter readiness inspection,” checking the items others have mentioned above. With modern cars, there generally aren’t any significant services that are needed to be ready for cold weather.
Coolant flush and fill is usually recommended at 30,000 miles or every 2 to 3 years with conventional antifreeze. With extended life antifreeze (e.g. Dexcool), the intervals are longer. It’s done to prevent corrosion; the antifreeze protection does not deteriorate (which is what is meant by “permanent” antifreeze – it doesn’t mean it should never be changed).
Most automatic transmissions also have a 30,000 mile recommended service interval, or maybe half that if a fair amount of towing or mountain driving is done. As mentioned above, this is independent of what season it is.