The snowmobiles (at the opposite end of town from the Missti Skip) are free to use, but you need three things before you can take one out: a key, some gasoline, and a place to go.

To get a key, check out the flyer stapled to the right-hand post near Dagny's spot; there's another one inside the Culture Center on the bulletin board to the right of the gift shop. Once you've done that, you can get a key from Elisabet on the ship.

Elisabet and the Ship

To get gasoline, you can find a large red gas canister inside the Missti Skip --

-- in the storage closet to the right of the kitchen.

What am I looking for in the storeroom?

When you have both items, use the gas can on the front end of the snowmobile (you can see the gas cap under the handles), then use the key (above the handles) and you're off.

As for places you can go, there are only two. One you learned about from the snowmobile flyer, and the other from Dagny when you fix her heater.

How do I fix Dagny's heater?

After you leave town, you go to a crossroads. Click on the forward arrow to go to the ice caves, the left arrow to go to the cabin, and the down or back arrow to go back to town.

Incidentally, the first time you use the snowmobile, when you come back to town, Gunnar will suddenly appear and be a little startling. No harm done, though.