So your trailer is winterized, has power from your house, and you are only worried about the battery? Correct?
As long as your battery is fully charged (trailer converter/charger is switched on and ~13.6v going to the battery) you will not have a problem. If your battery is discharged and the weather gets cold, then your battery could freeze.
(BTW, dealers are notorious for letting batteries discharge while on their lot.)
Sherm & Terry w/rescue Eydie (min Schnauzer) & Charley (std Poodle)
2015 Jay Flight 27RLS, GY Endurance (E), Days: 102 '15, 90 '16, 80 '17, 161 '18
2006 Ford F350 PSD, 4WD, CC, LB, SRW, Cmpr. pkg, Equal-i-zer 4-p, Continental ContiTrac TR