I lived in Northern Minnesota for 10 years, and during that time, I went out on my snowmobile often, in all weather, alone or in small groups of 2 to 4. My weekend trips included Upper Michigan, Northern Wisconsin, and of course Northern Minnesota forests. Each trip averaged over 100 miles. As with rental sleds, my snowmobile equipment compartment was about the size of a shoebox, and unless you have the optional luggage rack, or the optional trailer hitch, most of what you carry has to go in there, or in your pockets. When renting, it is essential to check and see that the OEM toolkit is in the compartment, and that all of the tools are in there. Snowmobile trailer tip over on forest trails at normal touring speeds.

This might constitute heresy, but rather than list the equipment in my PSK, I'll tell you what I actually used in 10 years and 5000 miles of backwoods travel.

Spare headlight bulb (hit a big bump, and they can burn out)
OEM sparkplug wrench
spare sparkplugs (sparkplugs foul often)
spare drive belt
magnetic compass and topo and trail maps
Leatherman Supertool (to remove barbed wire that had wrapped itself around my drive axle)and a million other things
Bic lighter (kept in my inner pocket)
Mini Maglite (also kept warm on my inner belt)
Helmet
Thin nylon balaclava (I got frostbit on my lower chin/neck crossing a frozen lake at -25. I never felt a thing. Balaclava complely eliminates this, and the thin nylon doesn't make your helmet too tight).
Thin cotton gloves (for detail work that you can't wear your snomobile gloves for)
A retractable saw (I used to carry a small hatchet, but they are unsafe on bitter cold days when your hands are cold and ice forms on the handle during use).
Clif bars or equivalent high energy food
instant coffee and tea bags
A metal canteen cup to melt snow for beverages.
Bandana
Whistle
Extra snowmobile key in an inner pocket

All of this will fit in your pockets or in the small compartment under the seat. Have a safe trip.