I live in a town where I don't have the space to build a separate building so I converted our 10' x 12' storage shed into a skinning shack. It's small, and gets crowded quickly when I'm thawing coyotes, but it works well and is easy to heat. Right now a small shop heater keeps it at about 12 degrees but when it's colder I need two of them going. If I had the option I'd go about 16' x 20' to have more room to work. You have to heat it so I'd consider that when thinking about what size you want.
I've had to find ways of maximizing my space however possible. Some of the ways that I've done that is by putting my winch with skinning base and freezer in my garage. If I only have 2 or 3 coyotes to skin I don't use the winch, it's only for anytime that I have lots to do at once. Hooks on the ceiling of my shed helps a lot with maximizing space, and having a fleshing beam and makeshift beaver skinning table that I can move helps. My beaver table is a small table saw with base and a small piece of plywood to put on top. When not in use the piece of plywood leans against the wall out of the way. I board my beaver right on the floor. I also do my checks everyday so I can put up fur a little at a time as opposed to a lot all at once and I try not to let my workload pile up.
I'd love to have room for a washing machine but for now, I wash my coyotes in a plastic garbage can and fill a 5 gallon jug with water in the kitchen sink and bring it out to the shed. Depending on how dirty/bloody the yotes are, I can wash up to three pelts with two jugs of water. It's a routine that I settled into but if I had the option I'd definitely have a washing machine to make my life more comfortable.
Here's how my shed started out:
http://www.outdoorsmenforum.ca/showthread.php?t=227275