The sugar content of the grass has little to do with its height, and there are a LOT of variables involved. Definitely check out the Safer Grass site (above). There is a lot of info, but it is worth the read.
Also I read that sugar moves up & down the stem during daylight hours so that there is less at night so putting them out on grass in the evenings & overnight is best if that's a concern. It moves down to the roots at dusk and comes to the tips in the morning or something like that.
From the sources I've read, the grass stores the sugar in the bottom 3 inches of stem/leaf. Therefore, shorter is sweeter.
However, if the grass is long and lush, mowing it to 6 inches or so would cut down on the sheer volume they can inhale in a given amount of time.
Ditto and further to that, when my area was in an "exceptional drought" and pastures were threadbare a few years back, my trimmer said he saw more horses hooves on starch overload during that time than he ever remembered in our county before the drought.
The amount of sugar made is directly proportional to the amount of sunlight hitting the leaves. Go out at midday and look down at some thick, taller grass. See how much sunlight is hitting the bottom leaves. Not much. Then go look at some short grass. Every leaf in full sun all day.
Of course, there are many other factors that confound this.
Well, we could compare my long unmowed pasture to my neighbor's manicured-like-a-golf course paddocks. And also compare the horses within. My two horses have ten acres divided in six paddocks, and get moved from paddock to paddock so they are never on real short grass for very long.
Neighbor's ten or so horses are on maybe seven manicured acres and never rotated. Grasses on both properties are the same, a mix of bahia and bermuda (with copius amounts of weeds over here on the sloppy side.)
Her horses, except for the ones that are so ancient they are thin from having few teeth, are fat to the point of foundering, have frequent colics, and lots of thrush.
Mine maintain a good weight UNLESS I leave them too long and let them guzzle all the short grass they want. Of course mine get ridden, hers dont.