snowtercycle 

The more appropriate way to refer to a snowmobile. It drives on snow, it has handlebars, and it has wheels (well, sorta), so there's enough grounds to put it in the bike family. Similar to calling a jet-ski a boatercycle.

I take my snowtercycle up to the slopes every other weekend to shred some powder.

snowtercycle by Fat & Furious February 6, 2014

snowtorcycle 

A motorcycle you ride in the snow.,

"Put your helmet on when you ride your snowtorcycle!"
"There's lots of snow out there! Let's take the snowtorcycles out for a spin!"

snowtorcycle by Pogmotoin March 2, 2009