The Hungarian Half-bred is among the top three best horses available in Red Dead Redemption along with the American Standardbred and the Kentucky Saddler. The Hungarian Half-bred looks like a 'white' horse with a dark muzzle, but is in fact what would be referred to as a "grey" horse. If you look closer to the colouration you will see that it is in fact a 'flea bitten grey' due to the numerous amounts of coloured specks covering its coat. This horse has the best resistance to damage as well as the best stamina, but its speed is slightly slower than that of the Kentucky Saddler and significantly slower than that of the American Standardbred.
A deed for this horse can be purchased at any General Store for $1500 ($750 with high enough Honor, or low enough honor at Thieves' Landing) after you have successfully broken the horse at least once. Deeds are not single use items. You can use a deed as many times as you like, and it will still remain in your inventory. Usage of a deed will allow you to respawn your horse in the event it is killed or when you would simply like to switch horses.
In the real world the horse was originally bred in Hungary, and specifically intended as a competition horse. The use of Hanovarian, Holstein, Furioso, Thoroughbred and Arab breeds have produced this fine sports horse, which combines strength and stamina with a good nature and intelligence.
In the game, the Hungarian Half-bred is described as a white horse with a dark face. However, in reality, truly "white" horses are rare, have pink skin and unpigmented white hair, though eye color varies (depending on amelanism or hypomelanism). Most horses usually considered "white" are actually light gray, as the albino genotype is very rare. True white horses appear completely white, with no gray (or any color) markings of any kind, unlike the dark muzzle and legs on the Hungarian Half-bred in the game.
The Unicorn from Undead Nightmare looks very similar to the Hungarian Half-bred, aside from the horn and cloven hooves.They even have the same spawn point.
There is an occasional glitch with this horse. While riding into Blackwater (the entrance that's takes you right beside Blackwater Graveyard), the horse will freeze briefly, then walk into the graveyard. This has been confirmed on both PS3 and Xbox 360.
This mount's extra health can be useful when attacked by cougars, as it is less likely for it to die in one strike, leaving more time for the player to kill the attacking critter.