Not sure how you brew your beer over there, but here the grains are removed from the ‘wort’ before hops are added and before any fermentation has occurred. So there is zero alcohol, yeast or hops in spent grain. Your steers will benefit more than your pigs from spent grain because they can digest the cellulose that the pig can’t. Spent grain should only be used in small quantities for pigs.
For storage you have to exclude air. I’ve successfully stored it for months using 1ton tote bags with a polythene liner. Fill, compress with a loader bucket, top up the bag and tie the neck of the bag. If you sit a sheet of plywood on top and weight it (or sit another filled bag on top) it will help compress and exclude the air. If you do this while the grains are still hot you’ll have very little spoilage.