Yes, you would switch out the reverse wire for the charge wire. To put a battery on the trailer you would just hook it up so that the horse trailers loads are drawn off it (trailer power wire goes to the positive terminal) and then your orange charge wire (or whatever color it is on the trailer side) would go to the positive terminal of the battery through a fuse like 30 amps. Don't forget to fuse the power line that goes to the trailer lights too.
2002 F350 CC SB Lariat 7.3 4x4 3.73 LS
Torredor Red, Viper 5701