At work we breed Nude (hairless) mice as well as many other breeds. They do have some hair as stated before only when they come from lines that have genes for both Nude and normal hair, such as Nude x het Nude breeding or het Nude x het Nude.
A Nude x Nude breeding does not usually have good results with offsping as many tend to die at a very young age because they at no point have hair to keep them warm, and sadly the female Nude mice are very poor mothers. They have the tendency to not nurse their young, so it is recommended to have a normal haired milk mother if you do produce Nude offspring.
That said... I would say the little one is actually displaying a form of skin disease known as Alopecia. It can be caused by many factors from allergies, parasites, chemicals, rash, and illness. It's when hair starts to fall out or not grow in completely due to some form of skin irritation. It's usually associated with an external factor, the most common two are mites and a buildup of urea or ammonia from dirty bedding. I would highly suggest segregating the mouse with a new clean form of bedding. Carefresh makes a bedding that is natural, not recycled, and free of chemicals. It is best to rule out allergies and dirty bedding before moving to parasite control. That would be necessary if you truly feel like keeping this one that is, but I would not suggest feeding it to any reptiles until you know for sure what has caused the skin irritation.
Good luck!