Hay that is stored properly will keep for months. It's designed to last all winter until the grass starts to grow again. Keep it somewhere cool, dry, airy and off the ground. It doesn't need to be covered particularly, as long as it doesn't get damp or is allowed to sweat in direct sun. Towards the end of the season, it may get a bit dustier and not smell as 'green'. It shouldn't be used if it is damp, mouldy or smells musty.