I accidentally killed the giant horse in BOTW
It appears that all horses will eventually respawn in the local areas where they are originally found, just based on other players' experience.
From a GameFAQs thread:
I confirmed that you can release the giant or white horse then find them again in their respective places.
And another GameFAQs thread:
So I released [the giant horse]. Then I checked if it respawns in Taobab Grassland and yes, it does (what a relief).