Free choice hay is considered healthy for a horse's digestion.  Quality of the hay is important - sometimes round bales can be dusty if they are not managed properly, at least it's true in my part of the country.

  One thing to consider is how many horses to a feeder.  For a large herd, dominant horses may keep the meek away.  Then multiple feeders may be needed.  I had an elderly horse for the last few years of his life who could not stand up to the herd bosses and needed different feeding arrangements.

 Everyone has given pretty much the same good advice.  Check the quality of the hay.  The only thing you might see is the horse get a "hay belly" from eating like a pig!  We feed round and square bales here.  The brood mares get the round bales and a couple square bales of rich alfalfa.  We have 5 mares to a pasture with 1 round bale, and we toss 1 bale of alfalfa in (1/2 in the morning and 1/2 at night).  We have thoroughbreds which require a higher percentage protien in the hay and grain as they have higher metabolisms.  Our QH and Paint mare in the other pasture has a real nice alfalfa mix round bale.  Our paint mare is fatter than a stuck pig!  She looks like a beer keg on hooves.  She will stand at that darn feeder and eat 20 hrs out of a 24 hr day.  The vet said she is healthy and eating for 2.  She is getting lots of fiber that is for sure!  I was exaggerating about the 20 hrs. but it seems like it at times. 

Just make sure your horse gets plenty of excersise.  If the hay is dusty or moldy say something.  They work for you!  The hay should have a sweet smell to it, not dusty or musty smell.  When you shake it the leaves should fall gently and it should not be stemmy.  Stemmy hay means they waited too long to cut it.  It is harder for the horses to eat and causes mouth ulcers from where it pokes them.   I will have to look up the website I used for my 4-H kids parents.  I sent it home with them to show them what good hay should look like.  I think it is the United States Dept of Ag that had it listed.   Since you board, they work for you.  If you aren't happy with the feed, say something.  It is your horses health!!

hay bellies are the result of horses eating stemmy, poorer quality hay rather than overeating.

Horses are grazing animals but remember that grass,especially in the spring, has a greater water content. So it take more grass to feed a horse than hay. It doesn't hurt a horses digestive system not be eating 24/7,espcially if they are eating good leafy hay- they are getting the nutritional value they need without eating so much they gain weight or dump the excess nutrients out the poop shoot. Personally, I don't feed round bales. I'd rather feed them according to needs.