all of the forces are down and inward from the weight of the vines and tension on the wires.
if youre referring to the side to side(west/east) forces from wind, there will be some, but its not like a fence or sail. there should be plenty of airflow through the vines even when they fill out. theres also a fence parallel to the trellis right there that will aid in blocking a lot of it. putting posts to a depth of 1/3 of its overall height is pretty standard.