I think tags could be a great visual organization tool when keeping track of projects like genetics, breed standards, performance stats, or countless player crossbreed projects. I think implementing or developing these features would help improve the current tags system:

Tags could be shown next to the name on a horse's page.

for example, Horse Fable already has base game tags, these being "Foundation", "Custom" and "Wild" ( these are at least the three I have encountered).  I propose that player tags could be shown next to these tags on a horse's page.

"Base Game" and player tags could be shown under a horse's name when viewing through your estate.

Additional tag settings to compliment these features:

"privacy settings" to include options to choose whether or not tags are viewable to the public, just the player, or viewable at all.  bonus points if more advanced settings include choosing which player tags are viewable to the public.