Q:

Can a car steer on a frictionless surface?

Do the front tires of a car act like gyroscopes, such that a car could steer on a frictionless surface?

A:

No, a car cannot steer on a frictionless surface. This has little to do with gyroscopic action and more to do with conservation of momentum: to turn, even when conserving its speed, the car needs to accelerate at right angles to its motion, which changes the total momentum of the motion. This change in momentum requires a force which, in normal roads, is ultimately provided by the friction between the tyres and the road. In the absence of friction, the car tyres would skid sideways with respect to their rotation (i.e. along the axis) without being able to influence the car's inertia.
It's important to note that, because of the gyroscopic effect, the car can indeed change the direction it's facing pretty much arbitrarily. The easiest way to accomplish this is to have a big flywheel, with a horizontal axis, inside the car, with a mass that's at least comparable to the car's. If you then try to turn the flywheel's axis within the car, you will instead turn the car around the flywheel, because of conservation of the large amount of angular momentum in the flywheel. (This will also cause a torque on the car about a horizontal axis, but this can be cancelled by the normal force from the surface.) However, even if you manage to turn the car 90° from its direction of motion, it will continue to move in the same direction as before, with its wheels skidding perpendicularly across the ice.
Also, as other answers have mentioned, if the car can interact with the air in any meaningful fashion - either by its air intake and exhaust, or by using its bulge as a sail, or by propping up an actual sail - then it will indeed be susceptible to external forces and it will be able to change its direction of motion. Similarly, the car would be able to steer if it could chuck rocks, bump off of other cars, or use rocket thrusters. I don't think this directly answers the core of the question, though.

A:

If the wheels had spun fast enough for a gyroscopic effect to become noticeable, the only result on a frictionless surface (which would be the same without a surface at all) is that when you turn the wheels, the rest of the car would rotate instead of just the front wheels :)
You need some reaction force to alter the trajectory, like a sail or surface friction or thruster.

A:

Yes you can
It is actually possible with a real car, but you would have to be very patient to steer a little bit.
Suppose you have built a car with power on the big front wheels to induce a gyroscopic effect. If you rotate the wheels, the direction in which the center of mass is going will not change directly, but the angle in which the rest of the body points will change.
Now we use another property of cars: Often they do their air intake in the front, and have the exhaust in the back. This results in a net force that is roughly pointed towards the nose of the car. So, as you can turn the car a bit by turning the wheels, you change the direction of this force, and will eventually be able to move the car a bit left or right.

