Well, there's a catch with all of this. The wheel has some inertia, so running in it should be easier than running the same distance on the floor. The ran distance is still the same , regardless of this fact.
And I'm trying to keep up with my jogging as well :)
A body also has inertia that makes it easier to keep running. The wheel may have more, but that also means that it takes more effort to bring it up to speed.
Also, one should take air resistance (of the running body or the spinning wheel) into account.
In physics it's generally safe to assume that all the different air resistances and drags and so on cancel out. You just draw a force diagram and everything always cancels, otherwise the hedgehog would have constant acceleration which we know isn't true.
Boundary drag on the wheel as it spins causes a loss of angular momentum, and so it slows over time unless force is applied (via adorable hedgehog legs) to keep it constant. Additionally, there are likely normal frictional forces at the meeting of the wheel and the supports, as I highly doubt they gave the pet a wheel with magnetic bearings in a vacuum.
And yes, the hedgehog must exert constant force in order to overcome this viscous friction.
On a related note, this viscous damping term scales as velocity, so the faster the wheel turns the harder the little thing has to work to keep it at a constant velocity.
And I'm trying to keep up with my jogging as well :)