Atopic Dermatitis. What you are describing is probably atopic dematitis or "eczema". This is a dry sensitive skin type that can be affected by dry winter air. Simple measures include no soap, bathe every 2-3 days only, daily moisturizer like curel. In some cases, medications are necessary/helpful. Consult your pedi.
Possibly eczema. Eczema or atopic dermatitis can cause dry, scaly, red patches of skin in susceptible children. Using a good emollient (lubricating lotion) two to three times per day on affected skin can be helpful. Good options are plain vasoline, aquaphor, or cerave (all available over the counter). Most children eventually outgrow eczema. Triggers include smoke exposure and over frequent bathing.
Dry air, eczema. Many children are prone to rashes when the skin gets very dry. It may be a common rash called "eczema". Try to increase the moisture to your baby's skin by using unscented, hypoallergenic moisturizers. Eucerin calming cream, cetaphil restoraderm, aquafor, and baby aveeno (oatmeal) lotion are some options. Sometimes a cool mist humidifier is also helpful by increasing moisture into the air as well.