My google foo is failing me.
I am booking travel in late December, early January and need to change planes. I have two reasonable options, Denver and Chicago. Prices/times are similar. Which closes more frequently in those months?
I presume your actual concern is missing a connecting flight, since it's quite unusual for an airport to shut down completely: usually they keep operating, just at lower capacity.
If so, you're probably better off with Denver, since on average it has both fewer delays for arriving flights and shorter delays for departing flights than Chicago O'Hare.