When horses pass away, we get an email stating so as well as a link to the horse but that link is broken whenever I get it. the classic Dooh page shows up! (edit: alright, well didn't know this was normal. It just just shouldn't even have a link then).

If the Horse doesn't have offspring it's deleted from the game

As River said. If the horse had offspring/living bloodline then they would appear. If the horse is passes and has no offspring/line they are automatically deleted from the game to keep space clear and not over run the server.