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The default bag of holding only has 10 minutes' worth of air in it, and it can only hold up to 500 lbs / 64 cubic ft, so I'm not sure you'd be able to fit a horse in one, living or undead.
This thread suddenly reminded me that I have not recently put random items into a normal bag of holding. A normal bag of holding found by adventurers should almost always have a bunch of other stuff in it, including other magical items (mostly potions and scrolls, but potentially non-consumable items). It's not like bags of holding are crafted and then never used, just to be found by someone in a dingy old dungeon somewhere.
Another option is to turn the bag of holding in to a portal onto another plane with a randomized location on the other side. Then, you just feel around for what is there and pull it out. You might end up at a market and find only vegetables and fruits, or you might be in a king's treasure chamber and find jewels and such. There could be a set number of locations for the portal on the other side to open at, but the location would be random.
Disclaimer: thought of this from a Raymond E. Feist character.