Here's a pretty good discussion of the issue. It still contains an error or two but is worthwhile:
According to this, current "wind chill temperature" is reported based on wind velocity and temperature only. Humidity, density of air, and radiation heat transfer have nothing to do with the reported number, although they obviously do affect the actual and perceived coldness.
As pointed out in this link, the wind chill factor was originally worked out for human faces (not human bodies). The wind chill factor varies depending on the surface it's applied to- so faces, wet rubber, and monkey heads all have different wind chill factors. The orientation of a surface in the wind would affect wind chill, so your face will have a different wind chill factor on the upwind side than on the downwind side (wonder which they based it on?) If you have a beard, the wind chill factor would be different. If you're fatter or skinnier, have higher or lower metabolism, etc, the factor would vary. It varies with height above the ground. Not surprisingly, different people disagree about how it should be defined- because it's not just a simple rate.
The equation listed in the link is:
Twc = 35.74 + 0.6215Ta - 35.75V^1.5 + 0.3275TaV^0.16
where Twc = wind chill temperature, Ta = actual temperature, both in F, V = wind speed in mph.