One possibility is that you have eczema. Eczema is an inflammatory condition of the skin characterized by dryness, redness, and itching. It is generally worse in winter months (as the cold dry air dries out the skin even more). It can generally be controlled through the use of a good skin moisturizer, preferably something thick and greasy like hydrolated petrolatum, which will trap in the skin's moisture better than a standard lotion, as well as using an over the counter steroid cream.
Another possibility would be psoriasis
, which is an autoimmune condition of the skin. Unlike eczema, the red spots in psoriasis tend to be more demarcated and brighter red, and they are typically covered with a very distinctive whitish or silvery scale. Sometimes psoriasis causes other problems as well, such as pitting of the nails and joint pain or swelling. The skin part of psoriasis can be treated with steroid creams, usually prescribed by a dermatologist
or primary care doctor
If the spots on your legs are more nodular feeling and deeper and painful, then this could be a rare problem called erythema nodosum, which can be associated with other underlying medical problems.
I suggest talking to your primary care doctor, who should be able to diagnose and treat this for you.