I have seen many portraits with people holding Ferrets and even Minks. Usually, the human in the portrait appears to be wealthy. I haven’t seen paintings with Squirrels as pets, but then I wasn’t going around in search of such portrayals.
Some landlords will allow their tenant to have Ferrets, even another animal usually seen only in the wild, Sugar Gliders, a sort of nocturnal Tree Possum.
Ferrets are good if you have a rabbit problem. https://www.youtube.com/watch?v=XerUmuPStyY
John Singleton Copley who portrayed a number of our founders and probably most famous for his portrait of Paul Revere, painted a portrait of a young Henry Pelham with a pet squirrel...