I agree with @Kusanar I always stand up my bales on end as well and cut the ties. Sheds, barns, garages even a mud room will work well to store your hay if you don't mind some hay stems laying around. 
I used to peel off a flake and throw it out to the chickens either outside or in their run. But this is wasteful as much of it never gets eaten and falls away into the dirt or bedding.
So what I do now is to pull off a piece of the top flake and shake it out over a feeding tub. I shake all the leaves out and remove the left over stems. I don't worry about getting every stem out, the birds like to eat a few of them, however whats left in my feeding tub is mostly all leaves. This system of separation only takes a couple minutes to fill a couple of feeding pans and nothing gets wasted other than the stems which there really aren't all that many in a quality bale. (If you keep goats, horses or other livestock, you might feed them the stems if you don't want them to go to waste.) A bale will last a very long time this way, especially if you buy quality alfalfa with a ton of leaves.

I used to peel off a flake and throw it out to the chickens either outside or in their run. But this is wasteful as much of it never gets eaten and falls away into the dirt or bedding.
So what I do now is to pull off a piece of the top flake and shake it out over a feeding tub. I shake all the leaves out and remove the left over stems. I don't worry about getting every stem out, the birds like to eat a few of them, however whats left in my feeding tub is mostly all leaves. This system of separation only takes a couple minutes to fill a couple of feeding pans and nothing gets wasted other than the stems which there really aren't all that many in a quality bale. (If you keep goats, horses or other livestock, you might feed them the stems if you don't want them to go to waste.) A bale will last a very long time this way, especially if you buy quality alfalfa with a ton of leaves.