Not quite sure I understand so just trying to get a bit more info to be helpful :) Are you saying that they are in a paddock that has no grass and get 2 flakes of hay twice a day? Is there a pasture with grass that they could be in? At our barn the soil is super sandy and its really hard to keep any grass in the pastures unless there is a lot of rain, which thankfully we have this year. Even with a lot of rain they don't get much grass anyway, they eat it down too fast. Our barn feeds t&a twice day with the horses getting 1 1/2 to 2 flakes per feeding. They also get grain (how much depends on the horse) Yes most of our horses are not eating all day because of the lack of grass which I know is not ideal but they are all very well fed and happy. Many of the boarders come out and let their horses graze in the unfenced areas (which have grass since there is not constant grazing to eat it down)
I have boarded at this place for years and though it would be nice to have more grass the horses have always been well fed and cared for.
The hay we get is from up north and is pretty expensive and no way the horses would need more than 4 flakes a day of it. plus it would cost a fortune to give them more.
I don't know if there is anything you can do, except pay extra for more hay.
If you are saying they are turned out during the day with pasture grass, can they just be turned out on the grass 24/7? why are they in the paddock 4pm til morning? Is it because they alternate the horses? If so then I think that much time on grass and 4 flakes of hay a day are fine, but I understand its not what you are used to, but what you signed up for when you decided to board there.
Hope that helps, just not 100% of the situation from your description.