The on-board power converter (breaker and fuse box) will charge the trailer battery if you are plugged into shore power. If you are not plugged into shore power, the battery is slowly draining, either by use or by parasitic draw (like your Co2 Detector or refrigerator electronics). So, if you are plugged into shore power, you don't have to be concerned about charging the battery. It just happens.
Now, if you cannot plug into shore power, most newer trailers are coming equipped with a battery kill switch. Depending???? the kill switch may truly kill everything the battery uses, or it may still be connected to some items, like the Co2 detector, causing a very, very slow drain on the battery called "parasitic draw".
If your travel trailer is going to be parked at an RV storage facility, then yes.... bring the battery home with you so it won't get stolen.
But if parked at home, keep it plugged it, you never need to mess with the battery... Summer or Winter.