That doesn't look like the stereo-typical cushings coat but I'll bet if the vet draws blood he will tell you this horse has a low thyroid.
Low thyroids on their own are rare in horses; it's generally something else causing the problem, like insulin
I'd almost bet money your horse is headed for insulin resistance.
I say that because I have two with metabolic issues and really think my third Tennessee Walker is moving in that direction
If he is, it's my pasture, without question. He wasn't shedding his winter coat like he should. His blood work came back showing a low thyroid. I put him on Chastetree and guess what -- within ten days his coat was shed to where it always is.
Good and not good. Not good because it took the chastetree to get his coat shed completely out and that, to me, means his got the beginnings of insulin issues. This is the same horse that was my Control Horse when I was involved in the University of Minnesota's metabolic studies two years ago.
Regarding the alfalfa:
My 25 yo with Equine Metabolic Syndrome is fine eating soaked timothy/alfalfa cubes because he's reached the age where he needs that extra protein and amino acids.
My 17 yo with true insulin resistance can't even smell those cubes or his insulin spikes.
If you can feed bagged hay (Tractor Supply sells it), my thought would get him off alfalfa for a month and see what happens.
Another reason horses can show a low thyroid and not shed like they should is iodine. Too much or too little will show the same symptoms however, so one isn't really sure which direction to go.
If your horse is getting a vitamin/mineral supplement he shouldn't be low in iodine. Without having your alfalfa tested, you have no way of knowing if the iodine is high or low.
We've reached an era where horse keeping, sadly, is no longer just throw a handful of oats and a flake of hay at the horse. There's so much pollution and feeds have been genetically modified so as to increase yield on less acreage that, it just about forces all of us horse owners to become more knowledeable horse nutrition than we want to be
And that nutrition is a delicate balance. While all my horses eat as if they had metabolic issues, once I get past the base diet, things really vary from horse-to-horse based on their personal health issues. It can make you crazy