On CAT II/IIIs the wind limits are such that the problem does not normally arise.
They are lower, but not all that much lower to be honest, head and cross 25, tail 10. Crosswind limit for take off (yes, i know, a different flight phase) on a wet runway is 25 as well. Some of those limits might be company reduced though or just lower because its for NGs, in the classics we flew manual landings with up to 40kts cross, but that isnt allowed with our NGs anymore, just 33 on dry runways.