If you (or other boarders) had pointed out the board as a potential hazard, then you might have legal ground to expect the barn to pay some or all of the vet bills. However, if no one (especially you) had pointed it out and asked for it to get fixed/made safer, then it's less likely you have any right to compensation.
Legal rights aside, as others have said- if you and your horse are otherwise happy there then I wouldn't make a fuss. Maybe take it as a reminder to pay attention to potential hazards and point them out to the BO before something else happens.
I recall on my boarding contract a line similar to "I have inspected the grounds and find them suitable for my horse's safety," though I suspect very few people walk the pastures and give a thorough look at the stalls before signing the contract. What's not written is that you should continue to make sure things meet your expectations for safety so long as your horse is boarded there. If something breaks or is added in a way you think is unsafe, speak up.
“The horse is a mirror to your soul. Sometimes you might not like what you see. Sometimes you will.” - Buck Brannaman
"Nothing forced can ever be beautiful." - Xenophon