Cows can do OK with as little as 5 lbs of hay per day(actually, as low as 2.5#, but that's pushing it!), so long as you provide supplemental nutrition in the form of corn, distiller's grain, soyhull pellets, corn gluten meal, etc.
Hay availability and quality was virtually nonexistent in our part of the country in 2007 due to a disastrous spring freeze and drought - no rain from May 10 to October 30. We started 'limit-feeding' - 10 lb hay/cow +10 lbs modified distiller's grain/cow, and the cows came through the winter in much better shape than they did in years past when they had free-choice access to all the crappy low-quality local hay we could keep in front of them.
We liked the system so well that we've continued it in subsequent years. Cows get 1.25 to 1.5 hours at the hay feeders - which works out to about 10#/hd/day - then come out to eat their distiller's grain. They pretty much stand around waiting for the next feeding, as there's really nothing in the 'sacrifice' paddocks they spend the winter in until they go to stockpiled fescue in January. Daily feeding, and requiring them to walk past us coming and going has done wonders to improve docility and handling ease.