It doesn't have fur anywhere else really. Looks like it does to the uninitiated or people that's been in Texas too long.

Yep, that looks like mange. I’d have just left it for the ravens here.

If I let it freeze solid for a day or two, that should take care of the mites right? Thinking it would be good to practice on, but I don't want mange

If you practice on a frozen coyote you may never try to skin one again.

Do not skin. Mande mites are transferrable to humans.

Sarcoptic mange mites can infect humans but I don't think it happens very often. Also, mites are host specific, so even though mange mites from foxes and coyotes can affect humans, the infection is self-limiting because the mites will not reproduce if not on their host specie.

I've skinned a lot of red fox with mange on the tail like that coyote in the picture. That's where it almost always starts on the fox around here, on the tail. If it hasn't spread to the back legs I put them up. I'm not throwing away an otherwise good fur because of a mangy tail.

I've never been infected.

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That is a sage statement if there ever was one!