You can feed whole flax seed and get the same effect. It doesn't need to be ground for the horse to get the fat/nutrients out of it, and it doesn't need to be refrigerated. I give my horse 2 oz of flax seed daily with his ration balancer (Triple Crown 30% Supplement), but you can definitely feed more than that.
The recommendation for Vit A for horses is 6,000-8,000 IU per 100 kg of weight. So, if your horse is 500 kg (1100 lb), he should get 30,000 to 40,000 IU of Vit A daily. In 1.5 lbs of Gro N Win he gets 33,000 IU, so he should be getting enough from that alone.
You should definitely provide him with some salt. Free choice loose salt is best, but can be difficult to do if he's not stalled. You can also add in some iodized table salt to his grain (I give my horse 20g daily) and also give him a salt block that he can lick if he feels the need for more.
I'm wondering if an iodine deficiency is the problem for him, as it can lead to a dry, lusterless coat (source
) among other problems. Aside from no access to salt, his diet seems sufficient as-is, so maybe try adding in some iodized salt and seeing if that makes a difference.