Goosebumps while running

Goosebumps are tiny bumps which appear on the skin of arms, legs, neck and other part of the body which has hairs. Goosebumps are produced on our body as a general response to fear and cold. In your case, I think the later is the more probable cause. While running or exercising, the sweat glands present in our skin becomes active, and a lot of sweat is produced. This sweat when evaporates from our skin, lowers our body temperature. This lowering of body temperature causes a cold sensation in our body, which may result in the formation of Goosebumps. Goosebumps are not contagious, and as such who have nothing to worry about. Wiping of the sweat regularly, might be an effective way of reducing your Goosebumps.

HI Jason,
You can get goosebumps while exercising for two reasons, the first being the body's natural cooling mechanism of sweat evaporating off the skin, causing a chill and thus: goosebumps. Researches have proved that the body produces 15 to 20 times more heat during exercise than at rest and this is the way your body regulates its core temperature.
The second cause is more serious: Heat exhaustion. A relatively common condition, symptoms can include severe chills and goose bumps. Other common signs include headache, weakness, dizziness, nausea, rapid heart rate, hyperventilation and extreme sweating. If the body is not cooled and the heat stress continues, heat stroke can occur, which can be fatal.