I noticed this with a asset template I created recently too. Went pretty far working on it so I saved it as an asset template and it broke the asset pretty severely. It certainly wasn't a 1 to 1 version of what I had previously.
My workaround that seemed to work was to avoid any nesting of Asset Template references. So I went to a previous version that I had right clicked on it in the hierarchy and chose "Unlink Instant Root." Then I did the same for all the children. THEN I saved it as an Asset Template and it worked fine.
Seems like a bug but maybe Horizon documentation tells us not to nest Asset Template references. 🤷