The tires you want for dry highway driving will have the least amount of friction possible, since that way you will get better gas mileage. In rain or snow, these same tires will perform very poorly. On the other hand, tires designed for rain or snow will have more grip, and will give you worse gas mileage. Tires designed for rain will push the water out away from the tire. However, in snow the channels that push the water out may fill up with snow, which will leave you with a tire that performs very poorly.
“All season” tires are a big compromise between all of these conditions, and therefore will never be the best tires for any of them. If you live in an area that doesn’t get a huge amount of snow (like say Maryland or Virginia), or you only drive on roads that are well maintained and kept free of snow in the winter, then you can get away with all season tires, which is nice because then you don’t have to have two sets of tires that you have to store and rotate around and all of that. On the other hand, if you are like the OP and live someplace that gets a lot of snow, you’ll do a lot better with a dedicated snow tire. You don’t want to use them year round though, since they will get poor mileage and will wear out fairly quickly in warmer weather.
Studs help to drive on ice, but they are very annoying when driving on dry pavement. If you routinely drive on really bad roads, you may want to invest in some chains. The nice thing about chains is that you can put them on when you need them and take them off when you don’t. The bad thing about chains is that it takes some effort to put them on and take them off.
4WD helps too, but you have to be careful. 4WD helps you go. It helps you turn a little, but it doesn’t help you stop at all. As others have mentioned, don’t go thinking that 4WD just always drives better in the snow or else you’ll probably end up in a ditch at some point. 4WD is also a bit tricky in the way that it recovers from sliding. With FWD (front wheel drive) if you just point the wheels in the direction you want to go and give it some gas, that’s not all that bad of a thing to do. If you do the same thing on a RWD (rear wheel drive) vehicle, you are most likely going to end up with the back end of the vehicle in front of the front end (wheeeee!). While the back end of a RWD tends to spin out if you don’t turn into the direction of the skid, RWD does give you an advantage over FWD in that the drive wheels and the steering wheels aren’t the same wheels, so when the drive wheels lose traction, you don’t lose steering at the same time. With 4WD though, turning into the skid or turning in the direction that you want to go can both lead to weird behavior, depending on how much you turn the wheels and whether the front wheels or rear wheels happen to grip first. If you aren’t careful, you can sometimes have the rear wheels push you in one direction and then have the front wheels grab and pull you in another direction, making a sudden snap turn of sorts.
With whatever kind of vehicle you have, one of the best things you can do is find yourself a nice wide open parking lot with no cars in it, and drive around skidding like an idiot. What you want to do is get a feel for exactly how and when the vehicle breaks traction and how it recovers as well. Then, when you are out on the road you’ll not only recognize when you are starting to lose traction sooner, but you’ll know how to recover from it as well.
The biggest key to driving on icy and snowy roads is to not make any sudden changes. No sharp turns, no fast stops, no fast starts. Plan ahead. If you see a light ahead, slow down in case it turns red. You can do a slow gentle stop even under the worst of conditions. Trying to lose a bunch of speed in a hurry though is only going to result in you sliding out into the intersection and getting hit. Also, leave a lot more room than normal between yourself and the vehicles around you.
Nothing grips on ice. 4WD doesn’t help you at all there, except maybe that with four drive wheels at least one of them may find a patch of road that isn’t icy and get some grip. The best thing to do with ice is just plan ahead as best as you can, and plan on driving at a constant speed straight across the icy patch. Trying to do anything else, like turn or stop on ice, isn’t going to work very well. Bridges often ice over before the roads around them do (since wind blows under the bridge and cools it down faster), so slow down and take it easy when approaching a bridge so that you can just easily and calmly drive across it.
If you have 4WD, read your owner’s manual to find out if you can leave it in 4WD mode on dry pavement or not. It puts a lot of strain on 4WD vehicles that don’t have a center differential if you drive them on dry pavement. You can wear out your tires much faster and can wreck the transfer sometimes as well.