Anhydrosis or anhidrosis is an inability to, or reduced ability to, sweat. It can be experienced by all animals that naturally sweat. (Note that dogs and cats sweat only through their paws and thus could be considered to have natural anhydrosis. There are even some human groups that do not sweat).
Anydrosis occurs in horses rarely, but often enough to be known. It is most common in Thoroughbreds and horses with a lot of Thoroughbred blood (I know a half-bred hunter with the condition).
The cause is not known and the condition can be transient or chronic. Transient anhidrosis is associated with asking a horse to perform in hot and humid conditions it's not accustomed to (and thus it's a common problem in show horses, especially eventers_. Chronic anhydrosis may be seasonal or all year round, and can sometimes be treated with amino acid supplementation. In some cases, though, only moving the horse to a cooler climate (not always feasible) helps.
In addition to not sweating, symptoms include an unwillingness to move quickly, loss of appetite and dulling of the coat. The horse may also pant excessively (horses do NOT normally pant the way dogs do).