I think confusion can be avoided if you are careful about what you mean when you say
The car is traveling at 60 mph
because velocities need to be specified with reference to some observer. An observer running on the ground will, for example, say that objects seem to be moving even if they are stationary relative to the ground.
When you say the above quoted statement, do you mean that in the presence of a 10 mph headwind, the car is traveling at 60 mph relative to the ground? If so, then relative to the wind. the car is traveling at 70 mph. However, if by this statement you mean that the car is traveling at 60 mph relative to the headwind, then relative to the ground the car is traveling at 50 mph.
On the other hand, if the statement in quotes is taken to mean that if there were no wind, then the car would travel at 60 mph relative to the ground, and if you wanted to figure out how fast it would go relative to the ground in the presence of a headwind, then you would need to know about the aerodynamics of the car. In particular, you'd need to know about its drag coefficient.