You can live in solar trailer same comfortably as in shore home - almost. Mostly it's a matter of "wants" than "needs". 3 big screen TVs running at the same time in different rooms, and lights all around the house whether you need them or not, is something you can't have with solar.
AC in summer is the only thing that IS a necessity in some areas and that trailer-sized solar can't handle.
Microwave it can, with enough batteries - and you can live well without MW.
Hairdrier - and its user - need to be controlled and kept on mid-setting, this is more about whims and having it "her way" than something necessary.
Powerful outside lights all night long is one of those things that I probably won't understand. Unless the area is unsafe (and then I wouldn't want to be there).
Electrical compressor fridge solar can handle, it's a matter of fridge size and power unit (12V is costly but more economic than 120V via inverter). 1600 Watt fridge like in pianotuna's rig is not very common - I think he is running an ammonia fridge on electricity, those really draw horrible amount of energy.