Ypedal,I can give some info on the subject of Skidoo's,I was the Skidoo mechanic and warranty repair mechanic for all Skidoo's in the Yukon for 5 years,so I know a few things about them...
First,all the battery does in a Skidoo is operate the starter motor,period. Skidoo models without electric start have no battery,and only use a regulator(that limits voltage to about 13-14v by dumping excess volts to ground,voltage keeps climbing with revs without one) in the charging/electrical system,in fact the lights and acc. are running on AC power from the motors charging coils. A model with a battery and electric start has a regulator/rectifier so the battery will be charged with DC current. Start the machine and check voltage at the battery terminals and at the headlight bulb socket to test generator output voltage at various rpms. I don't know if this will be correct for charging a LiFePO4 battery,maybe rig a charger into the system somehow if necessary...
Will Li-FePO4 hold charge for long periods in extreme cold,maybe how cold it gets where you live matters a bit...I think it will be fine,it only has to spin the motor for a couple of seconds to start it. You still have a recoil starter in emergencies anyway.
As for the stock Skidoo headlight bulb,they were a normal quartz bulb,I used to replace them with a higher watt bulb from the auto-parts store,a stock bulb is usually 55H/50L(Watts),a good replacement is a 100H/80L. I used these bulbs in my truck's Bosch headlights too and they really light things up! I wouldn't worry about the extra current draw,the generator is made to handle extra acc. like heated hand grips etc.
A good idea to lighten your sled!