All manufacturer's have to demonstrate the maximum wind conditions under which the autopilot can safely land the aircraft within the particular requirements (LOC & GS deviation for CAT II and Touchdown zone for CAT III). For example Transport Canada's Working Note give values for CAT II of 10 kt Tail, 15 kt Cross & 25 Kt Head winds as minimum values that must be shown.
If memory serves, the Boeing 777 ended up coming to Wichita from Seattle as they were able to find, & successfully land in, a 44kt crosswind. Considerable time & effort goes in to doing this testing - we ended up taking a CRJ to Newfoundland from Wichita just to get representative CAT III conditions.