IMO,
Unfinished pets are rolled skin on skin and frozen in a garbage bag (I use the little white flexible ones for house garbage's, they seal, and are easy to rip open). Thaw with bag taken off on cardboard to absorb moisture.
Finished pelts are always put in the freezer. No issues for short term storage, just make sure they are in a fur bag so they don't get stuck in side wall frost.
Long tem storage requires a more sealed approach (greater than 6 months).
If you leave pets out in a shop, basement, etc. the little black brown beetles will find them. You may get lucky, but likely you will have a problem. If they get on them, especially beavers or any pelts with a saddle, they will be destroyed. I speak from experience.
I finish beavers all summer. I dry for a week to 10 days on the board, then they go into the freezer....112 to go
Spruce