You would be amazed at the nutritional differences coming off the same fields from different cuts.
Some cuts can be very high in startch and sugars, this can be harmful to some horses. Especially those with I/R or founder problems.
Alfalfa is a good hay, but you want to know what your CA/PHOS ratio is.
Selinium, is a problem is a lot of area's, if your hay is lacking you may want to supplement.
Check with you feed store, some get testing done as a matter of course. If not, your local ag dept can do it for a few dollars.
And you thought all you had to do was find nice green hay......