As everyone has already mentioned they do.
Horse breeds are classified into 3 different "blood types:"
1.) Hot Blooded
2.) Warm Blooded
3.) Cold Blooded.
Now these different blood types DO NOT mean that cold blooded horses are actually cold blooded like reptiles and vice versa, (although there may be slight fluctuations in body temperatures). These "blood types" more so refer to a horses temperament.
Hot blooded horses are your Arabians, Barbs, and Thoroughbreds. They tend to be more high strung and spirited.
Warm Blooded horses are your stock horses (Quarter Horses, Paints, Apps, etc), Warmbloods (Oldenburgs, Hanoverians, Holsteiners, Selle Francis, etc), other types of "riding horses..." They can be spirited, but are more level headed in general.
Cold Blooded horses are more of your heavy-duty breeds - Draft horses (Belgians, Percherons, Shires, Clydesdales, etc). These tend to be very calm; nothing really phases them...
However, keep in mind that despite these "blood"/temperament classifications, there are exceptions. Each breed also has their own quirks and each horse has its own unique personality...
I know you said you were interested in the "Indian" breeds...
- Paints are very versatile. They are just like Quarter Horses only with "more color" ("color" = markings/white). In general, they have a very stable mindset and a great work ethic.
- Appaloosas are interesting... I personally am not a huge fan, but they do make a nice horse. They generally tend to be more stubborn and lazy...