Usually I mow my horse pastures high, around ten inches or more and have never had any problems. But I have seen small pastures mown/scalped with riding lawn mowers.
Anyway, it sounds like you are doing the right thing by scattering the clippings.
Yeah - thanks.... I know grass/yard clippings are way too hot for horses, and if they were following me munching out, I'd worry. The stuff I'm cutting is the stuff they don't like. And they dry up fast.