The higher the cruising speed of a plane, the less the wind will seem to blow it around. It has nothing to do with high or low wings, other than the fact that most high wing planes are designed to be lightweight slow flying floaters. Larger airplanes typically fly faster than small planes thus the seem to handle wind better. High wing planes that fly fast (quickie 500 racers for example) can also handle high wind.

A lot of trainers are very nose heavy for stability. The elevator has to be trimmed to fight that nose-heaviness. Because of this, any increase in airspeed (wind gust) not only makes the wing make more lift but also caused the up-trim of the elevator to pitch the nose up increasing the wing's angle of attack which results in a plane that "balloons" when a wind gust suddenly increases the airspeed. Planes with symetrical wings tend to be balanced closer to the wings center of lift which means that the elevator does not have to hold the nose up so much for level flight. This results in a plane that doesn't balloon up so drastically when the airspeed increases.