Get to the airfield an hour earlier than normal to make sure you have time to de-ice the plane properly. Don't do a rush job with a credit card, make sure you get all the ice off, and don't neglect the elevator.
Don't fly through a snow shower, it's really not very fun.
The only big issue of carb ice in winter is a taxi over wet grass when the temp is in the right range. Talk to an instructor and look at the carb ice table, found in many locations such as LASORS. In flight it's more common in summer temps, but continue regular checks as usual.