Like I said (and granted I'm not as constantly in the cold as you) I've never had a problem even with the small power starter even in the coldest, frozen conditions. I have a block heater, two battery heater plates, trickle-chargers, as well as a couple oil pan heaters and I can draw a good 10-11 amps from 120VAC

when fully plugged-in, total overkill I know for not living in the arctic, but it sure is nice to start the truck near warm in -40F.
Anyway, without any shore power, I've had my 80 buffet a crazy winter RAIN storm abreast that then dropped about 60F overnight in the oncoming blizzard. The whole truck was frozen to the ground and all of the inside of the engine compartment was packed with ice and hard snow, all the way up to the batteries. Took hours to chip the tires and frame out. Standard fare surely for you up there but my point is that even with the starter literally frozen--though it
barely turned--it did not exhibit what you're describing. I do think it is time to tear it down, regrease (?) it shouldn't take too much (?) but you might as well change those starter contacts...