Heat rash occurs when the sweat glands in the skin become clogged by dead skin and other debris. This is usually brought about by excessive sweating and chafing of the skin while exercising in hot weather. Typically treatment of heat rash includes good skin hygiene, gentle exfoliation, and applying an anti-chafing barrier product when running (there are many of these available from most sports or athletic supply stores).
However, it sounds like what you are dealing with may not be heat rash, since it seems to be provoked by cold and wind. I think this is more likely just to be straight forward chafing and skin dryness. Of course, treatment is partially similar, as using an anti- chafing barrier will be important. However, I think the key for you will be good skin moisturizing before and after running. Also, you may want to avoid particularly long or hot showers as these tend to dry out the skin even more.
If you try these approaches and your symptoms worsen or do not improve, you may want to talk with your primary care doctor
. Occasionally, reddened and itching skin does not respond simply to moisturizing and may require a topical steroid cream.