One of my first horse rides as a child made me pretty much swear off ever getting on one again. Stable it was not...

I hever never once heard of a dutch roll occuring to a train.

The rail equivalent is called hunting oscillation. https://en.m.wikipedia.org/wiki/Hunting_oscillation

Am on a Dutch train right now and there is a distinct lack of roll, Dutch or otherwise.

That said, I wonder where the term Dutch Roll comes from. Perhaps the oscillation is reminiscent of the motion of a ship rocking side to side. The Dutch were a major sea power.

When it happens, it's catastrophic, and then it is not called a dutch roll.