War Horse died, possible to get it back?

Unfortunately, you cannot get it back. Once a horse dies, it stays dead permanently.

This has been confirmed by several external resources, such as:

• https://guides.gamepressure.com/red-dead-redemption-2/guide.asp?ID=46968
• https://www.businessinsider.nl/red-dead-redemption-2-players-keep-killing-their-horses-2018-10
• https://gamerant.com/red-dead-redemption-2-horse-dead/

As described in the first link:

The situations described above can lead to one of the two results:

• Your horse is gravely injured. You can still safe (sic) the animal if you have the item described below.

• Your horse has died. You can't bring the animal back to life.

When it comes to the War Horse, Dappled Black Thoroughbred and Black Chestnut Thoroughbred, the "Special Edition Red Dead Redemption 2 Official Strategy Guide" says:

Note that horses exclusive to the pre-order, Special and Ultimate editions of the game are unique in that they respawn at the Valentine stable when they die.