Where I ride we are usually both dripping with sweat by the end.. Well, not so much the horse because I'm still a beginner so it's not too difficult for him, but where the saddle was is very sweaty, and sometimes his neck. My trainer tells me to rinse him off every time. Then I use the sweat scraper and we will usually stand in the sun for a few minutes while he grazes. He's usually not completely dry when I put him back, NEVER dripping wet though.. Never thought about this. I'm interested to see what others say.
"No hour of life is wasted that is spent in the saddle." -Winston Churchill
"Strong legs, soft hands, steady mind." (Unknown)