While cycling within some of the resort areas can certainly be done, there are no cycle lanes on the WDW roadways and they are generally very crowded with buses, service vehicles and private autos- not very conducive to safe cycling. I don't recall seeing any signs prohibiting cycling on the roadways, I also can't recall seeing any bicycles either- except the surrey bikes around the Boardwalk and at OKW.
There is a paved walkway from OKW to DD that could be used for cycling, but it is only about 1 mile and won't likely prove to be much challenge.