There are tables available that offer info on watering depending on the weight of the cow, air temp, dry matter feed constituent, etc etc. that all will affect the requirement for water.
I think that grass probably contains water. I know the content of a lettuce is mainly water based so it might be the same with grass. I know a lettuce can be substituted for water because they do that in the Arab world.
Obviously, give the cow as much water as he wants to drink.