12 gauge cord. the wire size of his extension cord.
as for the hose warmer. I dont have any experience with them but if they are anything like other low heat warmers it probably needs to be plugged for quite some time before it will work as intended
Try pre warming the hose inside your trailer/rv before you hook it up and plug it in. It might give you a jump start on actually keeping the hose warm
kinda like the crappy engine block heater on my truck lol. Doesnt really do much good if the engine is already cold.. But if i plug it in right after i get home it would do its job
2009 Sun Valley Road Runner 16ft
2010 Chevy Silverado 1500