I have never kept sheep so not positive about about how destructive they are but I think they just clip the grass to the roots . A horse though is really bad about spot grazing even in a large pasture with plenty to eat they will sit and nibble on something they like and keep pulling and pulling till they pull those roots out of the ground (they are especially destructive on wet grass )
I’ve had those stupid pea brained Arabian horses actually eat my cedar fence posts even when there’s plenty of grass or alfalfa ready for them to eat 24/7.