The launch-day release of GTA V on the Xbox 360 and PS3 does NOT include gambling or horse racing.
However there is a history of gambling in GTA, the ability to wager money is first introduced in Grand Theft Auto: Vice City, when the player must pay entrance fees for Vice Street Racer events, with a set limit on how much he or she can bet, and perform well enough in the races to break even. In Grand Theft Auto: San Andreas, more activities were available that the player can take part in to wager money on in order to gain more money if the player wins the activity or lose the money wagered if the player loses the activity. With its expansion in GTA San Andreas the chances of losing/winning are more probable.
GTA: San Andreas partly took place in Los Santos and had gambling, draw your own conclusions about GTA V post-launch plans.