I go snowmobiling up in old forge NY every winter. My family has been snowmobiling since the late 60's. I wear a goretex lined suit, jacket, and boots. It really works well to keep you warm, however I have been snowmobiling on nights where the temperature goes down to -15*F. Then it doesn't help as much, the wind feels like it goes right through.

Anyway, off the top of my head this is what we bring with us out on the trails, we always travel in a group of two or more:

-trail maps, compass, GPS, cell phones, two-way GMRS radios
-spare belts (snowmobiles are belt driven)
-spare sparkplugs
-spare fuel and coolant lines (these rot out and break)
-assorted tools (mulitools, flashlights, plug wrench, pliers, screwdrivers, ect)
-tow straps
-hatchet and fold up saw (sawvivor is great for clearing small fallen trees of the trail)
-nalgene bottle and steel cup or pot (carrying water off your body is useless since it just freezes, melting snow is the way to go)
-ferro-rods/mag bars/bic lighters (the bics need to be warmed up before use)
-hand warmers
-signal mirrors and whistles
-spare wool socks, thin gloves (you can't wear heavy gloves when trying to fix the machine), and spare facemasks.

I think that's it as far as what we carry on the trails. On the trailer we carry a lot more stuff so it something breaks we tow it back to there (or if we need something else that's where we go back to and grab it).

Most snowmobiles aren't made to carry a lot of extra stuff, saddle bags that can fit about as much as a daypack are most common, some have a little rack on the back that you might be able to attach a sleeping bag to. Even so, you really can't carry much more than a day-packs worth of stuff on there unless you're pulling a little sled trailer behind you.