Bubblegum on a Fur Coat?

Try freezing it off with an ice cube. Hold an ice cube on the gum spot and gently pick it off the frozen bits. It will take several freeze applications depending on the size of the gum wad, but it will work. Be careful not to smear the wad deeper into the fur by rubbing, just hold the ice cube on the gum wad, and gently pick away the frozen part. Repeat as needed to remove all traces of the gum. I've seen this work on fake furs and carpet, too:)

Fur is OK with being damp, the reason you don't toss fur in the washer is usually because of the construction method; the sewn together skins aren't preserved and constructed to take the thrashing a washer puts out.

Fur anything needs specialised handling to clean. But using an ice cube to remove a gum wad isn't enough wet or thrashing to damage the garment.