It sounds like one of my Basenji's (Bungwa) ears. He is losing hair in patches on his ears. I first put it down to him pushing his head through the wire fence but thinking back one of his predecessors had the same but also his nose as you describe. It's a very long time ago and i can't remember how we trated it nor what causes it. I'm off to the vet with him next week for a diagnosis and treatment.
I'll be interested to hear what your vet thinks.