Answer:
Most general problem: Homeostasis would be thrown off.
Explanation:
When a person sweats, they are trying to cool themselves off from a high internal body temperature, sweating when cold can make the person colder and make it even harder for that person to maintain homeostasis without throwing multiple body functions out of sync.
However there is a condition that is associated with Hyperhyrosis (increased sweating) that makes a person sweat when cold: cold sweats, however this is also concerning when a person is cold. But as long as a person has no other symptoms, it is no need for concern.
Other than that, organs can take damage. It would be like the skin going into goose bumps when a person is getting heat stroke, the organs are too hot as is the skin, but it is unable to let any response out to maintain homeostasis.
Cold sweats are also triggered by a fight or flight responce. So the main take away is that the body would not know how to react because Homeostasis has been thrown off.
