The making of a good quality hay depends on many factors. Mother Nature, of course, plays a big role. Rain can limit access to fields and can wash nutrients out of the hay once it has been cut. A best-case scenario would be to cut the hay and have 2-3 days of hot dry weather and then the hay be promptly baled.
Legume based hay should be cut before the plants are in bloom. The more mature the plant the less nutrients and digestible fiber it has. Grass hays fall into the same category. The more mature the plant the less nutrients that are available to the horse.
Big stemmy hay is just that big and stemmy and not very digestible, at least for horses. Ruminants such as cattle, sheep and goats have extra help from the rumen to break down the more mature plants. Good hay for horses has small stems and lots of leaves. Color is not always a good indication of hay quality. Horses will actually pick out the best parts of the hay. If you see a lot of wastage it may be because the hay is not of the best quality. Try to avoid moldy hay as this can lead to stomach upset and possibly colic. Dusty hays can cause horses to cough and can cause upper airway allergies.
If you have questions about your hay you can have it tested. This can give you a better indication of the quality and if it is lacking nutrients, which may need to be supplemented into the diet such as selenium. The University of MN Horse Extension has more information on hay analysis and where you can get your hay tested. Click on Horse Extension to go to their site.