Palomino Pleasure Ride is an unreleased song, presumably from 1985. The track was mentioned in a note Prince wrote to actress Jackie Swanson, who also appeared in the Raspberry Beret video.
His note reads:
Are u well today? I hope so. I am in Minnesota rehearsing 4 a World tour. I made a song about u and I sing it before every Tuesday’s rehearsal. It’s a cute little ditty entitled “Palomino Pleasure ride”.
Please send me pictures of u, I miss your smile. I am very happy now and I hope u are 2.
It is however unclear if any song with that title was ever recorded in the studio.