Tbh the longer you can go without I would say the better, cheaper, more natural and less dusty than hay. I wouldn't start feeding hay untill you notice and decrease in her weight, or your pasture is looking abit bare but since you have said it's so plentyful I doubt that will happen first.
The only thing I would watch is if the grass is very tall and plentyful watch out she doesnt over do it and end up with a sore tummy, but if she comes in to get riden groomed etc that should be a suficient enough daily break from grass.
In our field we electic fenced off a section at the bottom so once they grazed the field and it was looking abit bare we could move it back at a suitable rate to make it last abit longer so that might be worth a shot so you can watch she doesn't get to fat and decided how much you want her access too.If your field is big enough you could half it so when its done she can be swapped over letting the grass recover and then moved back and forth, though it is a wee bit late for much growth.
I'm kind of jealous you have such a good sounding pasture at this time of year ! Ha
ETA: I just noticed theres a post further up that someone has suggested the electric fencing and rotation stuff ah well I should read more before I post haha