How big is your trailer wire?
How much load is on that wire (running lights circuit)? How much capacity is left?
How many amp/hours is your battery?
Everything depends on these factors, and you haven't answered any of these questions.
I know you have a battery that's dedicated. When you use the winch then start your vehicle, the battery will draw current to recharge. How many amps is your tail light fuse? Better buy extras. By the way, your vehicle and trailer lights have to be on too, so subtract that from your fuse capacity. If you put a bigger fuse in, the wire will be the new fuse, and it will fry inside your vehicle.
Most car batteries rate around 50amp/hour. 1amp X 50hrs. charges this battery (from completely dead). If yours is a 10a/hr., one amp will take ten hours, 2amps take 5, and so on.
Charging with one amp, you will be driving with your lights on for a very long time, just to charge your battery.
Your tail light circuit wasn't designed to run lights and charge a battery. I do not recommend it but hey, it's your vehicle. Running a separate fused circuit won't jeopardize your vehicle's electrical system and you'll have lots of aux. power to run without a separate battery, if you like. Hope this helps.