I don't think that would cause hair loss, though. Are these mice petstore-derived or show mice? Often petstore-derived mice don't do as well on high-protein diets and will develop protein allergies which lead to hair loss.
Other possibilities are ringworm, mites, or another external skin condition.
If you could post pictures, that might help.
I hope you get it figured out.
BTW, Welcome! Please introduce yourself in the Intro forum!
They are probably getting too much protein from the dog food. Not be funny, but dog food is for dogs Mice need between 12-16% protein in their diet, around 12% for pets and around 16% for breeders, and too much protein will cause itchy skin and hairloss. A bit of dog food is good, they need their meat based proteins, but mice need mostly grains in their diet. Have a look around the feeding section and you'll see the kinds of things other people feed their mice. Me, I feed roughly 70% grains, 20% dog food and 10% bird seed.