I have a hoof oil that contain eucalyptus but is diluted by some other things. my horse does not seem to react to it and his hooves look very good after I have put it on. Unfortunately it hasn't really touched his thrush in his frog hence why I am wondering if putting a pure oil on it would make a difference :)
I don't recommend eucalyptus oil used as a replacement of tea tree, while similar, they've known to cause reactions.
I know first hand as we used to spray the horses over with diluted tea tree, we ran out once so replaced with eucalyptus oil, 5 mins later one of the horses were extremely itchy all over and puffed up like a ballon. Felt so bad. We quickly gave her a wash and it resided.
I'm not sure how it treats thrush, but if you do try it, maybe do a skin patch test thing on your horse to see!