Sweat in either a horse or human is all about heat transfer. Horse sweat to get ride of heat. The evaporation of moisture ( sweat) has a cooling effect, just like on our bodies. As the sweat oozes out of the pores it carries heat with it. Once on the surface ( skin) it evaporates and provides further cooling.
Heavier bulkier muscles will produce more sweat than lighter muscles. Also areas with more surface area ( more skin) will cool faster than areas that have limited surface area.
So one of the first areas to show sweat is between the legs on the rear of a horse. The outside of the hips have a lot of exposed skin that helps cool the outer part of the muscle. But the innerpart has very little skin, So it produces more sweat faster than any other part of the body.
The back of the horse under the saddle produces a lot of moisture, Because the saddle blankets prevent the evaporation of the sweat. Notice how a horse at liberty rarely sweats on his back, But a horse with a saddle is always wet under the saddle. That's because the saddle and blanket trap heat and the body works hard to get ride of it.
So we have a large muscle mass in the hip area, that has limited skin surface between the legs, coupled with the rubing motion that produces a lathery sweat. Especially if they are dirty or have a diet high in certain elements.