JPerrone,
A useful way of getting this is to think of a hot-air balloon in a steady wind. The balloon will go where the wind goes, but the wind is not blowing against the side of the balloon: the people in the balloon will feel no wind at all. If you were to hand launch an RC plane from the balloon and fly it, you would feel exactly like you would feel flying on the ground in a dead calm. People in open-cockpit planes flying in steady crosswinds don't feel a breeze from the side. If they did, the air would have to be moving toward the plane faster than it was carrying the plane sideways, and, unless the wind speed changes, that would be impossible. Similarly, the yaw string on a glider points straight up in coordinated flight in a steady wind, no matter which way the wind is blowing. A steady wind doesn't blow against a plane in the air, the wind is a mass of air in which the plane is flying. When that mass moves, the plane goes with it.
On the ground, it's an entirely different matter. Taxi straight down the runway in a strong crosswind and the wind striking the plane's tail will tend to make it turn toward the wind. That's because the friction between the wheels and the ground keeps the whole plane from moving sideways in the wind.