For a 1972 Airstream: if i plug the electrical hookup at the rear

into standard 110V outlet, will that keep my trailer battery charged all winter? Or do i need to hook a battery trickle charger directly to the battery?
If I leave the Airstream connected to my GMC Yukon at the hitch, will connecting the Airstream to the 110V hook up keep the Yukon's battery charged?
If i leave the Airstream connected to the Yukon at the hitch and put a trickle charger on the Yukon's battery, will that keep the Airstream's battery charged too?
Any ideas or info greatly appreciated. thanks, david