Prit P. answered 05/14/19
MD with Significant Tutoring Experience: USMLE, Med School Admissions
Sweating is one of the processes our body utilizes to cool our body. When water is released, the purpose is for it to essentially suck the heat out of the body. The answer to your question can be both exothermic or endothermic, depending on what we define the "system" as.
If we define our body as the system: Heat is leaving out body, therefore the process is exothermic.
If we define the surroundings as the system: Heat is entering our system, therefore the process is endothermic.
Generally the system will be defined as what we would like to focus our attention on, and in this case the system will generally be our body, and therefore sweating is generally exothermic.