The human beings previously called artists will still be around as humans and will still have jobs, even if it’s some other job.
“Artist” is a vague term though, and I think we’d still have a lot of them due to Jevons’ paradox, the same way ATM machines have actually caused the number of bank tellers to increase. Especially because it’s high-status for society to say they support artists, which isn’t the case for other service workers like bank tellers.
There is a niche for horse rides, though - they’re romantic and I’ve seen them as tourist gimmicks in different cities. Artists have a bigger niche, as AI art (so far) produces digital images and not, say, physical sculpture or paintings.