With rings, you'll inevitably end up with dead spots, just like you will with "bale grazing", probably even worse. Too much manure and wasted hay and far too much hoof impact in one spot, to prevent damaging the turf, even in "perfect feeding conditions", OR even when the ground remains frozen. If the ground isn't solidly frozen, you'll have it stepped into the mud.
By unrolling, you'll spread out the hoof impact from ALL of the animals, all of the time, and you'll spread out the manure and wasted hay residue as well, so that the existing turf can survive, and more likely, even THRIVE much more fully across the whole field. Isn't that the overall goal... to get the animals fed during the bale feeding time, but to also as much as possible end up with a pasture where they are fed during the bale feeding time that then also can thrive more abundantly during pasture growing season?
The drawback of course is the investment in time and equipment to accomplish that goal. No one will deny that the manure can be a valuable resource for the next and future season's pasture, IF managed properly (spread evenly across the pasture so as to fertilize appropriately, instead of simply piled up... i.e. overapplied... in a few select spots at a level so heavy that the pasture is smothered/burned until the applied fertility is diluted and broken down enough by time). Few will fail to recognize the similar value in the wasted (uneaten) forage residues, again, if managed properly.
So it really is about how willing you are to invest in the management of your resources, in order to maximize the potential for return on that investment. The way I see it, you can spend time and equipment to properly fertilize your pastures with a resource that you already have (the manure and uneaten forage), or you can "manage less appropriately" that resource, and then spend time, equipment, and $$$$ to purchase it elsewhere......... the choice is up to you.