Year-old hay should be fine. However a number of factors play into that. Hay keeps up to 3 years if stored properly -- out of direct sun and protected from enclosed humid environments. If it gets moist, it can get moldy and that's really bad. That can happen to even newly harvested hay. If it's baled with high levels of moisture, mold can develop. Moldy hay will smell musty, not fresh.
Hay also loses nutritional value as it ages -- mostly in the early months. This isn't a problem for rabbits because we don't want the hay to be too rich anyway. It doesn't lose much more after that first year. The protein, fiber, vitamins, sugars, and minerals, for instance, of 8-month old hay will be almost the same as 2 year old hay.
The older hay may not smell quite as fresh, so picky bunnies may turn up their nose.
In short, hay grown last year (and stored properly) should be just fine.