^^^this is false!!
first off, to the OP...Le Chatelier's principle deals with any sort of equalibrium rxn as it was derived as a concept on how equalibrium rxn's shift in order to relieve certain "pressures" placed upon it.
now for the reasoning behind why the Kw would have lowered with a decrease in temp. In order for a system to lower in temp, heat must be taken away via some endothermic rxn (evaporation for example like in your freezer). the process of the heat leaving the system is a result of an endothermic rxn, so thus the water in the OP's question will undergo an EXOTHERMIC RXN (shift to the left) in order to counter those effects (explained by Le C's principle). you can also deduce this another way...when bonds are formed, energy is ALWAYS released. this is what's happening in this problem thus making the answer to this question exothermic.
H2O + heat ----> H+ + OH- (remove heat, and guess what happens
)
i hope that made sense, i wrote it pretty quick. gotta go enjoy the sunshine!!
😎