Just like in the single player of Red Dead Redemption, you can call your mount in the multiplayer too. This is invaluable in free mode, and can be a real advantage if you choose to call in your mount during a competitive match. As you progress through the ranks, you can unlock new mounts which are faster and have more stamina.
El Señor
The first mount unlocked is El Señor, a mule which has limited stamina and poor speed. It is available to players from the initial rank.
Lusitano Nag
The Lusitano Nag is unlocked at Rank 4. This is slightly faster and larger than the mule, but is still a very poor mount.
Turkmen
The Turkmen is the third mount unlocked in multiplayer, at Rank 8. It appears visibly stronger and larger than the Lusitano Nag, and it is also much faster.
Cleveland Bay
The Cleveland Bay mount is unlocked at Rank 22. It has medium speed and stamina.