Depends on quality of hay, depends how it is fed to them, depends what other feed is available (and weather, copying CF)...
Like Castle Farm says, they ideally need good grass leaf, preferably early season. Feed the minimum at a time once you gauge what they need, if feeding small bales, since they waste loads (ungrateful so-and-so's), and for best economy use a feeder off the ground preferably under shelter (moving it regularly if you are really keen to preserve your pasture). If you are feeding round bales direct, I would bank on 3-4 over winter for 12 smallish sheep if covered from the weather and some other grazing is available, and keep mineral buckets out there. If you have a Mole Valley branch nearby, try them on 'Super Energy 16 plus fish oil' buckets out of amusement (£££!) - it is the ultimate sheep lollipop, they demolish tubs of the stuff and fight over it. Add in a daily dose of cake/nuts and they will be happy.
Technically, a ewe needs around a kg of dry matter per day, rising to 1.5kg in late gestation. Good hay is 80-90% dry matter, so an average non-gestating ewe would need 170-190kg of hay over a 5-month period... but as JS says, double it to account for wastage... I know, you do the maths and get 4 tonnes of hay for 12 ewes over 5 months. But, you'd be surprised at the weight of grass left on the ground and the contribution of supplements.. (and, the fact that us humans are odd in expecting to maintain our dietary intake over winter)...
Start feeding them when the grass has run down - maybe late Nov early Dec, and keep feeding until the daytime temperature reliably stays over 6degC again. Even if they are 'only' lawnmowers, if you skimp toooo much on feed then the pasture will be so depleted that the grass won't get going again in the spring before the weeds take over.