Running a cold machine for only a few minutes every so often causes condensation (by product of internal combustion) inside the engine crankcase etc.
If ur gonna run it like that, it should be run for about 20 minutes (full heat) or so to burn out the condensation from the internals. Otherwise you're collecting water in the oil fluids.
I never start my stuff thru winter, unless I'm wrenching on it.. I use (small) 1.50mA Battery MINDers on my stuff. My OE battery on my Panel truck lasted 11 years, & 7 years on my former Toro, sold with OE battery still doing & load testing well.