I went with my doom horse to the Hasrah Ancient Ruins, and the game prompted that one has to get off the horse to proceed with the quest. However, little did i know, as soon as i got off the horse, instead of been able to defend my horse from the Monsters, i got kidnapped into an isolated story instance, while my horse was been offered as a sacrifice...

If we are to be teleported unexpectedly, wouldn't it be reasonable to either let some option to warn about it to ensure horses are not put into danger, or at least dispawn the horse even if it is temporarily?

As the story progressed, I was completely unable to exit the instance, even by login off. So, I was forced to watch how the Horse takes lethal damage.

I believe that the horse death count are once again increasing counter, and even the NPC at heidle has a new audio stating that horse dead would make recovery more expensive after taking leathal damage. 

If you are prompted to get off your mount, you can be sure that you are going to lose control of the game temporarily.  I would advise staying on the mount and riding away to somewhere safe and then running back, if that's your concern.

I used a "traveler's horse" for that, since Woosa is just another alt to me, when that season was over.  I did manage to whistle it over once or twice early on (celestial calling horn), so I think it avoided death that way.

They're trying some new things with that awakening sequence.  I didn't like pretty much any of it.

Also, the horse death count does not have any influence on recovery prices. If there is such a voice line somewhere, it would be a relic of a long bygone era.