I operate a small 120v dorm fridge with an inverter. I have 300AH of battery capacity and 235W of solar charging. If the sun shines, all is good.
Travel trailers need a good, well charged battery if for only the emergency break-away function. In most States, it's illegal to operate without brakes for anything over 3000 lbs of trailer. If you don't have a built-in battery charger/converter, you'll need a stand-alone battery charger or rely on the towing vehicle for charging.
Solar charging with an RV makes too much sense. Size the amount of solar charging to your use and amount of battery capacity.