The bike trail at OKW follows the resort roadways, but also includes the paved pathway to SSR and DD. We've not seen a lot of people biking at WDW in general or at OKW, but it is doable.
At check-in, you'll be given a map of the resort with a jogging trail marked. Bikes may be travelled over the same path. The path to DD is no marked on that map, but is easy to find- just follow the paved path behind building 55 and take the section that turns to the left and follows the canal. (I'ts about a mile to DD from building 55.)
I would not suggest letting children ride on any roads outside of the resort (and would be very careful even there because of personal autos and buses). The WDW rodeways are way to busy with heavy trucks, buses and thousands of autos (with drivers unfamiliar with the roads- and sometimes their rental cars). There are no bike paths included on the roads.
Certainly riding from your villa to the pool would be fine - or riding to DD- but I'd be very cautious encouraging any other bike riding.
We are taking our bikes in Dec. not sure how we are going to store them but MS said it would be fine to bring them. I'll send the details when we get back.
