It depends how hard up you are for hay, and what you'd be willing/able to supplement it with.
If *necessary* (like, if it is all you can get) then TOTALLY nonmoldy non-mouse-pee-y year old hay is not the worst thing in the world. However, as Chirpy says, its main value will be that it is roughage -- which horses need a considerable amount of -- rather than being a particularly good source of nutrition (protein, vitamins). Numbers often tossed around for protein content of last year's hay are like 3-5% (as compared to 7-12% for this year's grass hay, or 12-18% for alfalfa; a mature horse not in any serious work usually needs something on the order of 11% protein in his ration overall).
If you can get some very high-protein forage, such as good straight alfalfa or alfalfa pellets, you can feed partly that and party the old hay (you might want to add an appropriate vitamin supplement as well) to get a reasonable semblance of nutrition.
Or a small amount of old hay, kept til midwinter or spring, can take some of the pressure off a limited supply of 'good hay' when you need to feed extra a) for warmth or b) to keep them from beavering your fences during the few weeks when they're sick and tired of winter and hay but the new grass hasn't started growing yet.
I wouldn't feed it without a pretty good reason, though. And it would have to be real cheap or I'd have to be real hard up for hay.
Hope that helps,
Pat