Quick Answer:  Sometimes.  It depends on the hay.  If the hay is soft and short then yes they likely can eat it with a muzzle on but if the hay is long or stalky then they will struggle and won't be able to get enough through a muzzle.

Some horses have persisted with hay and a muzzle and have developed some kind of technique to get some through.  Many don't though and then they will not be getting enough fibre and bulk in threir diet, this is especially true if the hay is stalky.

It might be worth a trial but make sure you are observing closely as you don't want colic due to not enough going through the gut.

I personally don't like it, it is not as easy as grass to eat and I don't like to worry about the quantity they have eaten.