Since ice packs at Walmart are so cheap, I’d suggest buying some and give it a try. I got some where the plastic is quilted so to speak so the whole thing is flexible. I figured they would be great leg wraps but so far I’ve only used them in picnic and horse camping coolers :).
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I have never felt that any freezer packs are quite as cold as real ice when I have an injury, or that they last as long in the drinks cooler as a huge bag of gas station ice, but then that is much higher volume. And you are only going to be icing a horse for 15 minutes not trying to keep steaks from going rancid while camped out in gorgeous open grassland with no shade 
My guess is there is not much functional difference between freezer packs for camping and for horse boots. If you distrust Walmart you could see if an outdoor gear store has slightly better kinds.
I think the only issue would be if the packs didn’t fit the pockets on the boots. The Walmart quilted ones could be cut to fit.
Quilted is the wrong word maybe. The pack is divided up into cube size pockets of coolant.