I think you are understimatimg them.
They do have quite a large frontal aera compared to the whole one of F1.
As well, drag is not only about that area, but also about its Cx, which measures, lets say, the quality of the shape of the entire car.
ANd there is where wheels are really bad. For starting, a cilinder is far from ideal in that respect, especially the back half, as it will create a low pressure region very prone to create undesired and very draggy turbulences and vortex.
To make it even worse they are rotating, with the upper part moving against the airflow, creating further friction.
All in all, while for example the new Mercedes E-class has a Cx of 0,26, the F1 cars in an average downforce confi are around 0,75 (although getting close to 1 at Monaco config)
WHat makes them different to cars, to have such a bad Cx?
Two things come on top: wings and wheels.
While wings certainly take a big part responsibility, they do have a good efficiency (ok, not as good as diffuser, but still have a correct shape, with a rounded leading edge, and sharp trailing edge. Only high attack angles make them really quite draggy).
On the other hand tyres, as explained before, are horrible.
The shapes of the F1 bodywork are more efficient than road cars too.
So most of it is coming from the wheels, though I can't recall the exact %. Bear in mind that Le Mans cars are quiet similar in wing sizes, yet have half the Cx of a F1. EDIT: I found that the wheels have a 60% of aerodynamic inefficency, and account for over 40% of the total drag of a F1. That seems very reasonable.
Also the fact that they generate lift, forces to use more wing angle to compensate, so furthermore drag as well.
Anyway, my point is not really about how much is the impact of tyres in the total drag, but rather how to reduce this impact by using covers for example.