Another option of controlling feed & providing more exercise is the "paddock Paradise' system, which may be a possibility for you. Google it for more info.
I've only personally used a grazing muzzle on one pony once, but I tried hard to make it work & she always managed to get it off, whenever I wasn't looking! Admittedly too, this was before they were readily available in tack stores here & it was a home made leather one.
I have seen, and have a few clients who have used them successfully tho. Generally on ponies that can wear them & run with their mates, who would otherwise have to be penned. It is always a good idea to supervise the first few wearings of a muzzle, make sure they are subsequently regularly checked and removed for some portion of each day.