IIRC, the danger in feeding grass clippings to horses is only if they are collected in a bag and given to a horse directly. They start to ferment in the collector and the quantity is greater than what they would be able to graze naturally. Even so, I've seen several people on this forum say that they've fed grass clippings to their horses for years without any issues (although I'm not recommending it)
A freshly mowed field in and of itself shouldn't present any particular danger to a horse- especially if the clippings are either collected and removed or mulched, but clippings left in the field won't ferment like clippings in a bag, and the horse still has to move around and pick out the clippings.
I think the OP's question was more along the lines of what would be more effort for her horses to eat- long grass or short grass. It depends on the design of the grazing muzzle you're using, but I think long grass is generally more difficult for a horse to eat through the muzzle.
The ideal solution, as someone else mentioned, would be to have a dry lot or very sparse pasture to turn the horses out on and limit the access to lush pasture.