A word about snow tires: The reason you only use them in the winter is because as the weather gets hotter the contact with the pavement at a higher temperature wears them down far faster than regular tires. I don't know anything about the winters where you live (I'm Canadian), but my advice is that if you're going to have snow on the ground for most of the winter then get the tires. If there will only be snow on the ground sporadically then it probably isn't worth it because your snow tires won't last long.
Some good advice on this thread, basically go way slower than you think you need to, and especially when taking turns or stopping start braking waaaay sooner than you would expect until you have a better idea of how your vehicle handles in snow. Just be cautious until you know how to do it. Slipping on ice is a lot like hydroplaning, because in both cases your tires have lost contact with the road surface. Don't overcorrect, don't panic, just ride it out and brake gently. Keep survival stuff in the car, especially for your kids. If you do go off the road you want them to be nice and warm until someone comes to get you. By survival stuff I mean warm clothes, a blanket, some water (this one can be tricky because you don't want it to freeze solid and explode, and you'll need a way to warm it up... candles!), kitty litter is a great suggestion.
Depending on how cold it is out, let the engine block of your car heat up before you start driving. Make sure your windows are defrosted and clear of ice/snow, as well as your side mirrors. This sounds obvious, but brush any snow off your roof and the hood of your car. When you start to drive the snow may get blown up onto either your front or rear windshield and because it's warm it will stick. And after all your hard work de-icing, you now can't see out of your windows again.
My last point is actually a good attitude to have while driving in any condition. Drive defensively. By that I mean drive based on the assumption that all the people around you are going to screw up. If you have the right of way and someone is coming up to a stop sign, have your foot on the brake in case they leave it too late and slide into the intersection. If you know someone is going to fast, quickly plan out how you're going to avoid them if they start sliding towards you.
Anyway, that is how I drive in the winter. You just have to be a lot more cautious and alert than usual.
