personally i prefer to remove the battery and store in a reasonable temperature. either charging periodically or with a tender on it. Leaving it in the trailer and the trailer plugged in is also a viable option, personally i prefer not to do that as and issue with the shore power line (tripped breaker or something eating the cord) and your going to end up with a dead and frozen battery.
as for the propane, no need to disconnect, just turn of bottles incase their is a leak that develops
'14 XLR 395AMP
'16 Ram 3500 DRW, 6.7 cummins w/aisin trans and 4.10 gears