Yeah...I can imagine. :( I think you'll probably end up having to put something on the muzzle, too, because the hair is just going to keep getting rubbed however fast it grows back from the vaseline. Maybe you can try wrapping it in something soft like maybe a cloth or vetrap or even duct tape or something if you don't want to buy the fleeces. Is the muzzle strap nylon? And is your horse turned out 24/7? Otherwise I don't see why she has to wear it when she's not grazing.
He knows when you're happy; He knows when you're comfortable; He knows when you're confident; And he always knows when you have carrots.