I'm mowing with the lawnmower. Yes, there are lots of cuttings left, but they are the cuttings of the weeds they don't want to eat living, and they seem to avoid them cut also. They've been grazing where I haven't mowed yet. The clippings are thick in spots, but I kick and spread them. Thinking of resting the pasture awhile now anyhow, untill it rains and can grow up a bit.
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.