I did the same plot for the three winter months, individually, and interestingly, January got the best fit, with R^2 of .47, followed by February at .43 and December "only" at .27.
Just speculation of course from my side, but is the reason to this "lag" that the pattern established in October is affecting the Stratosphere, which in turn is feeding back to the Troposphere and this takes some time?
1984/1985 is maybe a good example here, where we had a -1,8 OPI, followed by a very mild december, before there was a big freeze in January and February (as predicted by OPI)