I would just continue to brush, everyday even if possible. Dry air in the winter can cause dry skin, dander and shedding. Bathing would only further dry out his skin because it washes away the natural oils in his coat. You can feed egg more than once a week- perhaps 2-3 times... I would also add some canned fish in water. I buy the generic brand sardines and my pups LOVE it.
Especially in the winter in the colder areas, excess bathing will really dry their coats out..You can try using some baby wipes, unscented..I do that a lot....I do feed mine a raw egg once a week and also sardines, mine really love those
Living in a tropical climate with higher humidity Britneys coat does very well with daily wipe downs from mom and every other week bath. (this is one boxer that has too get used to water and baths. She has had no choice since she was 8 weeks) Using Oatmeal based works wonders on her. I have started feeding her egg a few times a week.
However, as others have said, living in a dryer place they cannot have so many baths.