Travis is mostly right.
You likely have an open differential. This is standard in most vehicles.
Vehicles need a differntial, because when you turn, the outside wheels have to travel farther than the inside wheel.
The problem with this is when, as you've discovered, one wheel slips, it just spins and the other doesn't. The energy is transferred to the wheel with the least resistance.
There are several fixes to this. The most common fix is a limited slip differential (also known as positrac, truetrack, etc.) It uses clutches to limit the slip between the wheels.
Other types include torsen which uses gears, locker which uses locking plates, and spool which is a solid connection (no differential).
Changing the differential is a drastic measure. Easier measures would be to use snow tires and add weight over the rear axle.