Of course, my Harry is living proof.
Are some animals cute?
Most of them are yes.
Lot's of animals are cute ! My Basset Hound is the cutest guy you've ever seen. Lot's of squirrels around here that are cute and fun to watch. I could make a long list of cute animals.
This entirely depends on your justification as to which animals are cute or not.
People tend to actually justify cute animals by their fur. Like Robin's answer with Harry. And I'll admit...I'm one of them. Any animal that has fur has a more likely chance to be cute to me haha.