If you can, get a front-wheel or all wheel drive car, rear wheel sucks in the snow. You don't have to have the heaviest car or an SUV in most areas, but generally a heavier car is easier to handle in the snow. Make sure you have good tires! They can make a huge difference.
Drive slow- I've hit patches of black ice that were under snow and put my car in a spin. Only reason I've not hurt myself is because I drive ~15 mph slower than the posted speed limit (not slower than 'normal'- it's NY, we speed everywhere). It's easier to get/maintain control of a car that isn't going that fast.
If you lose control of the car, try to react as if you were hydroplaning. It's a similar feeling/situation.
NY wants 1 car length for every 10 mph you're doing (ie: 40 mph = 4 car lengths distance between you and the schmoe in front of you). Double that in the snow, especially if there is already a good amount on the street and it hasn't been plowed yet. You never know if someone will lose control of their car or if they have to stop short. Also remember to leave a bit more of a stopping distance between you and the car in front for added safety.
It's also the law to clean off the snow off the top of your car before driving it. I know it seems a bit silly, but I had my windshield smashed from the snow/ice mix from someone's roof just because they were too lazy to clean it.
Really, driving in snow sounds a lot worse than it is. Just be careful and take it slow.