You should generally be good to go. You should take care to ensure that the battery gets properly recharged when you're done using it, either by running the generator or by having a solar setup (or both). Depending on the converter/charger you have, it may take a very long time to recharge the battery via the generator; a good standalone battery charger or an upgraded converter could make hours of difference in generator runtime, particularly if what you have is a single-stage converter. (I'm assuming you do not have a shore power connection available, or you would not have mentioned the generator in the first place.)
Take care that the generator exhaust cannot get into the RV--don't put the generator under the travel trailer, for example. It would also not hurt to ask around and make sure that whatever kind of generator you get is one that will not be too hard to get started in freezing temperatures.