I don't personally own an ATV (my brother does), but I do own seven snowmobiles. The four that we typically use I keep loaded year round with certain supplies. That way, I don't have to worry about myself, or anyone else, using them without basic supplies on hand. Very dangerous to be without any supplies in the middle of winter. I also make sure to check all my supplies before and after each season, as part of my regular maintenance.

Off the top of my head, this is what the sleds have in them:

-Spare drive belt
-Spare qt. oil (two stroke)
-Spare spark plugs with plug wrench
-Spare recoil string (on sled without electric start)
-Spare fuel line/coolant line
-Duct tape
-Mini WD-40 can
-Chemical handwarmers
-Tow rope or strap
-Surefire G2 LED flashlight (perfect for snowmobiling; LED so no bulbs to break, lithium cr123 cells that work well even when cold, and plastic body instead of metal body so you can still hold it in your mouth when cold)
-Leatherman Blast Multi-tool
-Bic lighter and Swedish FireSteel
-Metal cup for boiling water

That's the bare minimum. The two lead sleds (the ones that go out most often) are also equipped with a small combination survival/first aid kit that includes some other little odds and ends. One of the lead sleds also has a hatchet, while the other has a Sawvivor saw. (As there have been times when we've needed to cut down fallen trees with the larger saw, or chop through ice with the hatchet)

I often ride with other people and I even check out their gear. I won't ride with anyone that doesn't have at least a spare belt, spare plugs, and a flashlight. Often times I end up having to remind people that they have to fend for themselves when snowmobiling. Many are programmed with the notion that, if anything happens, they can just whip out their cell phone and call AAA or whatever. That doesn't exactly work out in the sticks, where you rarely get any cell service and land lines can be miles away.