It can be pretty tough on horses' stomachs. We had a foal with joint ill/ bone infection who got it for several months and the vet eventually had us give her breaks from it-- I think she was on it for five days off for three? Something like that, anyway. She never showed any ill effects from it.
Not too bad long term in humans - teens use it for acne for years at a time and do ok. Taking with food/feed will minimize some of the GI upset though it shouldn't be taken with vitamin supplements.
The worst I've seen is some serious 2nd degree sunburn for people on it if sunblock isn't used. Also most drugs when they "get old" don't really become harmful - just less effective. Doxycycline is actually harmful once it's expired, so make sure you have non-expired product.
A horse at my barn was on it (twice) for Lyme, and it seemed to affect the texture and color of her coat (sort of dry and more bleached/patchy than usual).
Thats interesting, my filly had doxy April/May last year, her coat went like skin, like she was clipped. When she finished the doxy she grew a thick coat in June, while wearing a rug. Went back on doxy in July and now in the middle of winter again has a really thin coat that looks like its clipped. She is rugged so possibly it would be different if she wasn't rugged. I've been wondering if it was due to the doxy.