I assume you mean a receiver hitch when you say Reese hitch.
Easiest thing to do would be to mount the winch on a platform that interfaces into the receiver hitch. They are available commercially.

I have my truck set up with a receiver hitch front and back , with wiring for the winch at both places. I can then set the winch at either end.

If God wanted you to walk and carry things on your back, He would not have invented stirrups and pack saddles