Is it your only pasture, or do you have another that you could toss the horses out on for a little while while it grows back?
Super short isn't ideal, but if you can give it a break, it will grow back! (Just look at any hayfield - around here at least, they cut them super short, but as long as it rains a little, they bounce right back.)
What happens with a short mow is that unless there is alot of rain, it tends to kill it off when things get dry. If its too short now, water it if you can and keep the horses off of it and let it recover as much as it is going to. Do that now, before the really hot dry weather comes in.
Does your tractor have an "arm" that allows you to raise and lower the deck? My John Deere GT requires you to raise the deck, then turn a knob to whatever inch setting you want. I just leave it up to do pastures, but also give the grass a couple days to recover a little before turning out on it.
Well, it is good for reducing ticks, but bad for concentrating worms, so pick your poison. You generally want to try to leave it around 4" but I totally get the dilemma -- I only have a garden tractor as well and am pondering what to do about that. 3" is much better than the 1" a former BO used to do, drove me nuts. I'd love to have a bushhog, but still waiting for a money sack!
Grass that's too tall isn't much better for the overall health of the pasture. Producing seedheads is an "end of life cycle" for most grasses, so you'll slow/stop blade production after a while if seeds mature.
What KIND of grass do you have? Various types have various requirements for lowest healthy mowing height.
I did find reference to "don't use tall fescue if mow heights will be less than 1.5"" , but others where it seems 2.5" is the lowest you'd want to mow.
HOWEVER, that is not talking about grazed pasture. Wherever you mow down to, horses will chomp it lower for a while,and that's where the damages start to occur.
Mowing greatly reduces ticks over unmowed, so you'll be ahead of the game just by mowing. But the lower you mow, the less shade the root base will get in the Summer, and the less healthy the underground roots will grow. Taller blades require deeper roots.
So, for us, our lawns even get cut high in the Spring, even if it means mowing more often, to encourage a longer/deeper root system for when the rains stop.
I mow the pasture pretty high - 5-6"
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I mow my pasture with a riding lawn mower all the time, and have for years, without a problem. On the highest setting, but I do put it down from the park position. I only have a couple of easy keeping horses and a couple of sheep, so I'd really be okay with wasting forage and killing some grass, but it hasn't seemed to make much of a difference. And my critters all have negative fecals.
So not worth it for me, but obviously your situation may vary based on climate, stock rate, worm load, and so on.
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Most grasses hold their "growing" reserves in the 2.5-3" of growth. There area few varieties that hold their reserves lower. If you tape into these reserves you can damage the regrowth of the grass. Another thing that can be an issue is that shorter the grass the highter the sugar content. Depending upon your horses it could cause some health issues. In rotational grazing operations farmers perfer not to graze thier pastures below 6" and usually do not turn livestock out till pastures are at least 12" (of course depends on the stocking rate).
The essential joy of being with horses is that it brings us in contact with the rare elements of grace, beauty, spirit, and fire. ~Sharon Ralls Lemon