The stomach can become cold during exercise because of a few different things, but the most common is dehydration. A dehydrated person may feel cold or get goosebumps following exercise, and it is a message from the body to drink water or get fluids into the body.
It's possible that a person could become cold after exercising because of being dehydrated, according to Seek4Fitness. When there isn't enough fluid in the body, less water and blood are transferred to the skin, making the skin feel cooler.
When people exercise, heat from their muscles is transferred by water to the skin, where it is turned into sweat. If there isn't enough water, it's possible for the heat to stay in the body but for the skin to feel cold or clammy.
When exercising, those who are dehydrated may see goosebumps. These tiny muscles are contracting and letting less water out of the skin, helping the body keep the water it has inside. Cold skin or goosebumps could both be a sign of dehydration.
Another possibility is that the air where a person works out could be cold. Skin is often exposed during workouts, and it can be chilled by the outside air. That can also account for goosebumps or shivering.