Dani...there's a couple of things you have to worry about with your car.
1) You kit hangs kind of low, so you take a great risk of going through a carwash and getting your kit ripped off from underneath, or you getting hung up half way through the car wash. Definitly not a fun thing to happen.
2) If you can make it through a car wash ok, then it's still a bad idea because of the brushes. Most car washes use stiff bristles on the brushes and it puts small microscopic scratches in your paint that over time, makes your paint look like crap. The only best thing to do is to go through a brushless car wash like it was mentioned above.
3) Go to a hand wash car wash where you hold the the spray gun and you blast the dirt off. Just wear gloves and a good jacket when doing it because it's still cold when you do things that way. But not as bad as if you were out in your driveway doing it by hand yourself.
4) Do it by hand. Just get a bucket of hot soapy water and when your hands get cold from washing, stick them in the hot water. *lol* And use gloves when you dry the car with a towel. That way you'll stay nice and warm.
Good luck....