"downtown disney" itself is an outdoors pedestrian mall. Its small and no bikes allowed
But in the outdoors disney general area.... i'm pretty sure its allowed... but i wouldnt recommend it.
1st.. not sure theres any place to put it
2nd... a lot of cars... all of the confused "where am i going" type that dont really seem to have a grasp on where they are going
3rd.. anyplace you wanna go.. all for pedestrians
But if you are okay not locking it up and feel you can dodge cars and not going into anything "disney" sure