Definitely don’t do aspirin long term – that’s an old school way of doing things and you’re right, it’s not good for your horse. Aspirin, and other NSAIDs (non-steroidal anti-inflammatory drugs) like bute and banamine are really hard on your horse’s stomach and can cause ulcers if you feed them too often/too long. I learned the hard way after I had my horse on daily bute for years for his navicular, at the advice of a vet who didn’t know (or didn’t tell me) about the harmful side effects. Luckily, I now have a vet who believes in supplements, and all three of my horses are on a daily joint supplement (they’re all different b/c they have different needs). What type of work does your horse do?