Wet catches, dry before skin & flesh??

So I'm looking for advice/input.. I mainly use drowning sets and it's pretty cold here most of the season. I've got a small shed to work in with NO Heat. Currently I dry critters best I can and hang em to finish drying. They usually freeze before drying.
My question, is it necessary for critter to have dry fur before the fun work, will wet fur dry while on wire stretchers? Not enough room to hang whole beavers in house to dry. I'm talking coon, beaver, mink, rat, otter maybe an otter this year. Some go in freezer after skinned.
I've read archives, may have missed conversation about this.
Thanks guys

They need to be dry. Here's what I do...as soon as you're done with dispatch, toss them in the water to soak while you do your remake. When you're done, slosh them around a little to get the chunks of mud out. If it's a beaver or muskrat and you have snow available, rub the critter all over the snow, it will be almost completely dry in less than a minute. Not sure how that works, but it does. When you get home, dry them as best you can, however you can (towel, newspaper, whatever). Then comb the fur in it's natural direction and hand them by a front foot so the water can run off. Put a fan on them, and they'll be dry in a day or two, they wont go bad in that time. When they're dry, comb them REALLY well in BOTH directions, it's important to go in both directions, that will get all the dried mud/sand/whatever out of the fur, there's no need to wash the fur. Never skin or flesh wet, you'll push mud out of the fur and it'll get all over the leather, your skinning equipment, and your fleshing board, and it'll be a huge mess, and you'll never get the mud stains out of the leather.

Yeah that's the answer I was thinking too. That's pretty much my process but they freeze before they dry completely then I get ice & holes. I've probably just gotta do a better job trying to dry em, maybe a little buddy heater with the fan. Thanks