Horse Browser writes Trails to disk as you go, so under normal circumstances you don't need to back anything up. Quitting, crashing, and updating all leave the sidebar intact.
If you'd rather have an extra copy in a different place anyway (entirely reasonable), the export takes about a minute.
Export a Trail as Markdown
Select the Trail and go to File > Copy Trail as Markdown. The whole Trail is now on your clipboard as plain text.

Save it as a file
Paste into any text editor and save it as a .md file. Keep it wherever you keep important things: Drive, Dropbox, an external drive, a USB stick.

More
The import/export guide covers the inverse: pulling that Markdown back into Horse later, on the same machine or a different one.



