In addition to the benefits, there are challenges with bale grazing

When bales are grazed, there is a loss of nutrients and dry matter to the hay. Fluctuations in climate and winter temperatures will cause hay to absorb moisture from all directions. Without a good freeze, the bottom of the bale will suffer from saturated ground. Mesh-wrapped or plastic-wrapped hay will cause less loss than twine-wrapped hay, but the wrapping can also be difficult to remove if conditions freeze.

Does this mean you will need more hay to make up for the loss? Maybe, but if there's still grass to graze on, maybe not. Fortunately, lost hay returns nutrients to the soil. It also leaves bare spots where the forage underneath the bales is suffocated. It may grow back if allowed to rest, or it may need to be reseeded when the seasons begin to change again.