I found a couple of 50-foot contractor grade 10-3 extension cords are a yard sale gobbled them up in a heart beat.
I wouldn't use less than the #12. I also would only use a long RV30A-15A 30AMP adapter (WALMART) and stay away from the little black round plastic adapters. They will get hot on you pretty quick and burn up your connectors... Steer clear of those cheap RED ones from WALMART...
DO NOT USE THESE
I have one of those 120VAC Receptacle type AC VOLTMETERS plugged in inside the trailer. This has the SAFE ZONE identified in GREEN.
We run our air conditioner and other appliances all the time in my two trailers. Being only 15-20AMPS you have to watch what you have on and sometimes can't run two things at the same time otherwise you will trip the breaker.
The other thing to double check is make sure your garage receptacles is wired to all three terminals so you can use all three terminals. Your trailer ground only comes from the the garage connection so that is important to have. Some extension cords may have the ground connector cut off or only two wires types.
Hook it up and turn on a few things then check your connections for heat. This is what you don't want to happen to your 30AMP connector.
We hook up to our garage connection all the time here when not one the road...
Roy Ken