Question. When storing stretched and dried muskrats and mink for a couple of months in the fall/winter is it better to keep in a basement at 60-70 degrees or in a garage at 10-30 degrees?

I would opt for the colder temps in the garage.

Garage as long as it stays 30 or below. You don't want it getting humid/damp/wet. Hopefully your garage is dry. Make sure you hang them from wire in a such a way that rodents can't get to them.

I keep mine in the garage and keep a fan on low blowing around them. Hanging on fur hangers from the rafters, to help avoid mice.

I store my rats in totes. All other fur is bagged and placed in a no operative freezer.
I don't get the rodent thing I have left fur laying on my benches for weeks and have never had any rodent damage. And I know I have mice in my shop.

We have a cool room downstairs, stays about 50° year round. We hang our dried furs in there until we sell them, no issues ever. It is very dry in that room though. Humidity will be the biggest issue I think.

I've had mice chew trails through my hair-on, stretched and dried deer hides. They were rolled into 8 inch tubes, maybe that encouraged the mice to nest in them. I don't want to take that chance with furs.