You should not run the A/C, heater, water heater, refridgerator, or any other appliance with the cover on. All those devices require that heat and/or exhaust be properly dissapated outside the trailer, and that cannot happen with the cover on. Personnaly, we make sure the battery is disconnected when the trailer is covered.
2012 Keystone Outback 277RL (Salty Doghouse II)
2005 Ford/Quigley E350 4x4 Van 6.0L Diesel (Moby)
Molson (goldendoodle-11yrs) & Zeke (parti poodle-6mos)