I can only remember flying in conditions that bad one time.... up in Petaluma, Ca. All of my flights, since I'm only a recreational pilot, are in very good weather.
But yes, you have to make cross wind landings to get your license. So when going thru lessons when those days hit with strong crosswinds the instructor will call you in for a lesson.
Cross win landing are very similar to using 'slip' to lose altitude quickly....that's 'basicall'y using full rudder, depending on the wind, turning the plane sidways... at which point it will drop considerably... then hold it until you've reached the altitude you should be at. Example? At Fresno Air Terminal, a few timess, the tower contacted me after I was already in the landing pattern asking if I was capable of a short field landing... (other traffic coming in and just to speed things up)... which meant I was too high and had to lose altitude quickly... Kept my downwind altitude the same, as well as the base leg... but then on final did a slip to drop to the proper altitude, similar to a crosswind landing, at least in attitude, but obviously less rudder and more aileron control.
And yes, I've had passengers questioning why in the hell I was so 'sideways'.