My best guess is they'd vomit if it was too much for their tummies.
Regular dehydrating reduces the size of the food considerably, but freeze-drying doesn't reduce the size much (if at all). I took a piece of a freeze-dried chicken (Pure Bites) and soaked it in water. I didn't notice it getting any larger once saturated.
They'll probably be fine. All I'd expect to happen is diarrhea, hard poop, or perhaps they'd vomit due to the quick diet change.
Of course, keep an eye on them just in case. Theoretically all the food should move out of their tummies and into their bowels within 12 hours, and I'd imagine it'd leave their bowels in another 12-24 hours.
I have to put all my treat baggies into a tight-sealing plastic container. I prefer the kind that twist to close rather than snap together. Otherwise my guys will sniff out the treat bags and team up to tear them open! Bad kitties! Yes, they have accomplished this feat before.
I'm sorry about the loss of your horse. That's very sad.