Should I leave my Travel trailer plugged in or not?

Leaving it plugged in is not necessary. By doing so you are leaving it vulnerable to power surges that could damage your converter. If you choose to be sure you use a surge protector. However, there is no need to have it plugged in unless you are planning to use any of the 120 volt appliances. I would also disconnect the batteries for storage. If you have a charger you can charge them a couple times during the winter. Batteries that are charged will not freeze.