The question I have is if the charger that comes with the trailer is a smart/3 step charger?
as for charging the battery, use the battery disconet every time you are not using the trailer, that will avoid battery discharge.
I have a 10w solar panel with a little morning start smart charge controller that keep the battery on my boat 100% charged when Im not using it. I intent to have the same set up for the trailer, it works great.
Never leave your battery outside charging during freezing temperatures, that will kill the battery for sure.. I lost a brand new AGM ($$$) battery that way....
Ricardo & Luciana Carvalho
2006 BMW X5
2016 Roo 23IKSS
Nights camped in 2016 - 22
Miles rode in 2016 - 6001