Yes it is OK to use the adapters. For home use it is of course better to install an outlet which matches what your trailer uses be it 30 or 50 amp. If you need to use the 15 amp adapter remember to only use those 110 electical appliances you actually need lest you trip breakers. Running the fridge should not be a problem. While it may take a while to get cold especially inside a hot trailer, you should be able to tell shortly if it is getting cold.
If you need to use an extension cord make sure it is a heavy duty one.
2016 Newmar Bay Star Sport 3004
2015 Jeep Wrangler 2DR 4WD Sahara, Automatic, Hard Top