You're going to want a nice really very flat road, since you'll be using solid, wooden edged wheels (I suspect wooden spokes wouldn't help the ride much, and would significantly add to the complexity).
Assuming that a direct drive to the wheel isn't attempted (eg a wooden ordinary), then they're going to have to either use a series of wooden cogs, or a wooden chain and pair of gears. That could be fiddly to produce, and probably needs quite large links to ensure that they're strong enough.