Probably not. Cold temperatures are a main cause of raynaud's phenomenon, so cross country running can trigger symptoms. If a person has only mild symptoms, and can keep his hands, feet, face, and ears warm with the newest gadgets (such as heated gloves and socks), and he only runs on warmer days, he might be ok. If he is running in the winter, anything can happen. Vasospasm can occur during or after running.
Related 2 excercise. The disease is primarily related to temperature changes in the extremities causing arterial vasospasm. Exercise will not help it however maintaining constant temperature of your extremities by wearing gloves when cold, and minimizing exposure to temperature extremes will help quite a bit. Ask your dr. About a drug called Pletal (cilostazol).