Quick Answer:  Yes your horse will be able to drink with a grazing muzzle on - if the following poings apply.  1  Make certain that the muzzle can fit easity into the water source ie bucket, tub or trough.  2.  He must find it easy and not be afraid of getting caught up. 3. You will stay with him until you are sure he can drink.

Some grazing muzzles are not brilliant for drinking, they can get very soggy and slimy which horses hate.  The softer ones like LiteBite do not hold water and it just flows out cleaning itself at the same time.

Soggy muzzles like some of the basket ones can be, also get very heavy and mud gets stuck in there as everything is held in.

Choose a grazing muzzle that allows the water to flow out easily and not collect grass and mud in there.