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So you are sucking a lot of cold dry air into your throat and lungs which drys out the natural mucuses that exists there, and causes temporary inflammation and pain. This results in that burning sensation you feel in your throat/chest/lungs, which may or may not be accompanied by wheezing and coughing. It can be quite painful and quite distressing, but usually, it should subside within, hmm, about 15-20 mins after you stop exercising.
3. Dry Throat. It is possible that the burning sensation occurring in your throat is being caused by dryness and irritation. Low levels of humidity in your home could cause the tissues in your mouth, nose, and throat to become dryer than usual.