I remember watching a traditionally animated movie maybe 15-20 years ago on a VHS my parents made by recording TV. I think it may have been a series of short fairy tale segments, although I can't be sure I'm not just remembering multiple movies recorded on one tape.
One scene stands out strongly in my mind: it's nighttime, the sky is dark blue, and there's a woman in a diaphanous robe sitting in a (roofless?) gazebo with Greek marble columns. I'm pretty sure she was a unicorn, but she'd taken on human form. I have vague memories of her being separated from someone she loved. There might have been a V/O of the text of a letter she sent him, or maybe her lover was there, and they were saying goodbye? There was definitely dialogue happening. Either way, the scene was very wistful, and I've never forgotten the music that was playing in the background. It was very emotive and bittersweet. After watching the movie, I immediately ran to the piano and learned to play the tune. I can still sing it, if that helps at all.
I'm running on the assumption that it was made in the 80's or 90's (before 1998 for sure), but my memories are foggy and it could have been an older Soviet piece. The movie that was recorded after it on the VHS was a dubbed Soviet adaptation of The Wild Swans.
P.S. - It's not The Last Unicorn.