Yes, the problem is that over the winter the grass doesn't grow and replace itself. The only solution is to keep them off it over the winter, or to do this now and re-seed, though ths will now take 2-3 months to re-establish well enough for another onslaught.
I keep my girls I their run until after lunch, by which time they have finished laying, then I let them out on grass for a couple of hours, confined within a circle of chicken netting ( well, all except Saffron, the Leghrn, who helicopters out when she has found all she wants.) I move the netting on to another patch of fresh grass every few days, to let the original area recover. I have three main areas that I rotate like this, and so far (several years) they have stayed grassy. The hens do look forward to their daily feed of grass, but don't mess up the garden too badly, and they always troop back ino the run for their evening mash, and seem quite happy in there the rest of the time. They have 12 sq. metres of run between 4 of them so plenty of space.