Surely do wish I had a bag of tricks.
Throw a tarp over the tractor also and hook up a battery charger. That will help get the whole thing warmed up.
Think about making a battery maintainer a permanent set up.
Then check out all the switches etc. and battery posts. Check fuses and remove reinstall relays. Use some dielectric grease on them. Heat gun can come in handy when doing this but don't melt the plastics.
Wife's hair dryer would also work but make sure the shed has enough room for a cot and one of them -30 C rated sleeping bags.
Note: I never follow my own advice??