[@Lauder] You [i]can[/i] buy mounts. I don't know how you would get that mount down into the dungeon or if it's a good idea but maybe we can put it in the imaginary rowboat?

In all seriousness though it's highly likely the mount would stay in Waterdeep which would mean it may not have much use mechanically. You could bring it into the dungeon with you and if you can solve the logistical puzzle of that, along with some rolls, in which case it might be very useful. Or maybe if you'd roll badly it'd fall to it's death. 

~The wonders of roleplaying games~