only items that run from battery are my rear brake lamps and indictators, everything else is AC stator feed, its a 2004-2005 sym jet ( red devil / basix /eurox), if i kill the motor while riding the only thing that works is brake light and indicators, No running lights front or rear will come on. and the stator on these struggle to run those lamps let alone charge the battery to its a very fine balance. also being over 10yr old and still on the same original stator i cannot risk burning that puppy out , hence im even holding back on a LED running lights upgrade.
Your power issue is worrying, have you tried a new stator or cleaned yours up to check the contact points. Ive followed a scooter whos lights dimmed at every stop, very dangerous. Heat wise then heated grips combined with bar muffs is what ive used the last few years. Cold can still get inside the bar muffs as they are really a wind jammer rather than a mitten. If you can invest then this year i bought a decent set of heated gloves! The wires are a pain but i can live with that for four months for the amazing warmth. Someone suggested plastic bags which sounds silly but actually are waterproof and windproof but need to be wrapped tightly. I've heard that Mechanics rubber gloves under biker gloves can give a good tight insulation layer but ive never tried that. My recomendation is invest in heated gloves. These are wired directly to the battery but draw no power until the gloves are plugged in.