there is your answer there, unknowns and federals, you've got mixed axles, low tread, wet weather and you let off mid corner; a lovely concoction for mayhem
might also be worth checking tyre pressure alround, should be 35psi alround if they are out it can have an adverse affect as well. also if the hnadling has thrown you slightly might be worth getting the geometry checked out and have it setup again, shouldn't cost more than about £60 but well worth it.
once you learn to use it to itsw full potential its a very rewarding drive. i'd take it steady at the moment with the snow regardless of what tyres your own you'll be wanting to go steady. if its really icy i'd suggest going a gear higher to reduce your torque available save the rear coming out without warning.
welcome to the club