I suspect it's too much
protein, &/or other nutrients that are particularly high in your lucerne that is the problem. Horses need proteins, as do the rest of us, but they don't tend to do well on high protein diets. As someone else said, it's also very high in Ca which can upset the phosphorus ratio too, if not fed as part of a well balanced diet.
I would consider 1st cut, stemmiest as the most suitable for horses. Often hay advertised as 'horse quality' means rich, whereas horses tend to do better on 'poorer' more fibrous feed.
Originally Posted by TbLover
Does anyone have a good mineral supplement in mind?
It depends on what your horse is getting from her diet as to what may be lacking. I personally think the feedxl.com program/service is great for that sort of question, if you don't want to consult an equine nutritionist directly.