Looking at car hauler/trailer, need some dimensions, please.
If the new to you trailer was built in the last 10 or 15 years, it probably has brakes on both axles and a break away system on it. If it doesn't, adding brakes to it will be easy. Given that the roads are probably salted a lot in winter where you live, you'd be better off just buying loaded backing plate assemblies to replace your brakes anyway. I do that even where I live. The cost difference between brake shoes and hardware, vs shiny new assemblies is not enough to even fight brake springs....let alone crud and rust.