I'm guessing you don't run a studded track? All of my sleds are studded just for that reason. I was riding an unstudded 340cc fan-cooled years ago and the back end went out while I was riding along an icy curve.

Luckily, I counter-steered, hit the brake, and it kicked back in line; but after that I studded all my sleds. It makes a noticeable difference in traction and handling. Like snow-chains for snowmobiles if that makes any sense.

You just have to remember to change to a slightly deeper set of carbides as well. This is because, on certain sleds, studding the track will cause it to grip too much in the rear and make it understeer slightly (which isn't as bad as snap oversteer, but it can be an issue), but changing the carbides to match the studs you're using fixes that.

Anyway, hope you feel better. Snowmobiles can be very dangerous. I figure snowmobiling along trails is often tantamount to playing a game of "dodge the trees."