Doubtful. More like three or four.
Ten each for a 25,000 man army would be 250,000 horses. I suspect even heavy rainfall can't produce that much grass.
Yes, 3-4 horses per warrior seems reasonable for a Mongol army on the move. But ten horses per warrior seems reasonable if you are looking at the number of horses in the Mongolian homeland.
The census of the Bogd Empire in 1918 showed about 1.1 million horses against roughly 640 thousand population. Just guessing, but if you figure one warrior for every six persons, you get a ratio of about ten horses per warrior.