Just so you know, you will get the mount across all characters on that server, but the stats of the mount are per character. So if you start training your riding skills (in stamina, capacity or speed) the mount will ONLY have those stats on that character. If you make another character, you will need to train your riding skill on the toon to get the better stats.
The stats are actually attached to the character, so if in the future you choose to purchase another mount (crown store or in game stable), that mount will have any stats you trained in already. (since the stats are actually part of the character, not the mount)