I learned last year about hay testing on here. Equi Analytical was recommended here on the Forum. I found them on line, copied off their form to send in with my sample. There is more to collecting hay samples than just grabbing a couple of wisps off a bale to mail in if you want a comprehensive test!
They recommended using a hay sampler probe, getting hay samples from 20 bales or so, that came from all over the hayfield. My sampling was a bit more “redneck” because the least expensive sampler was $ 150. I took a handful from the center of about 25 small bales, chopped it up, mixed the cut pieces to mail in. Tight big bales may be hard to get samples out of the centers where it is still green hay. They want about a half-gallon bag full to test. I used a cardboard, photo-mailing envelope from the post office to mail in the bag, form and check. I figured the stiff cardboard would protect the bag, not let it get punctured.
I got the test with 28 (I think) items. They emailed the results fairly quickly, 2 weeks I believe. Then I had to learn how to read the results! I Googled “how to read a hay test.” The University of Minnesota Extension came up and I learned from their site. They were very helpful in explaining things, saying the range needed in nutrients for good nutrition. My hay tested pretty well, right in the good numbers range for everything, just high in sugar. We have no obese horses or other health issues, so the high sugar was not a problem for my horses. We were very pleased with how well the horses did on our (first time hay balers) hay. They actually consumed less bales, looked VERY good, and used a minimum of grain and wet beet pulp, vitamins, from last Oct to almost June this year.
Trying to monitor hay nutrients in a boarding situation might be difficult. Does your pony’s hay come from a special pile of bales or from the main storage area? Did owner buy all the bales from the same supplier? And hay nutrients can vary between cuttings if farmer fertilizer the fields over summer. We put fertilizer on in Sept because the soil test said we needed more minerals after taking off hay last summer.
I would say if you wanted the hay tested, you will need to send it in yourself. BO will not see any advantage to herself in getting it tested. Not going to raise her income, so not something to spend extra money on. I was very curious about our hay quality, after buying some really poor hay for a higher price. Hay “looked good, nice green, soft, no dust” and it sure fooled us!! Had no nutrients either!! Horses looked poorer than expected, needed extra volume of wet beet pulp to fill them up, more grain than we ever used before. They are normally quite easy keepers.