If your car loses traction in first gear when you are trying to start from a standstill, you can try to start in second gear instead. If this does not work you can try to reverse a little before attempting to move forward once again, as this often gives the tyres better grip.
You should normally drive in as high a gear as possible in slippery conditions. Doing so reduces the risk of the car losing traction, as the rate of acceleration decreases every time you change into a higher gear.