Subject: Crosswind affects drag (and hence power req'd) on a car?

The 'crosswind' is taken as blowing perpendicular to the road the 
car travels on. For the same road speed, does the car require 
more power to maintain this speed in a crosswind than on a still 
day?

I believe the answer should be the power required does *not* 
change (since relative wind velocities can be resolve in mutually 
perpendicular directions), but my physics teacher thinks so 
otherwise. So who's right?

Re: Crosswind affects drag (and hence power req'd) on a car?