It probably doesn't have as much to do with removing or adding moisture as it does with the fact that most things contract when cooled. The fibers might just contract enough to run more smoothly through the machine.
We do this all the time when changing wheel bearings on our motorcycles -- freeze the new bearings overnight first and they go into the races with fewer issues.
However, I'm not sure how long the benefit would last with thread -- it would seem that it would warm quickly and you'd lose any contraction you had from it being in the freezer.
So, I'm with the poster that said "Use a quality thread and you won't have as many issues." :-)