If it were me, I would wait until spring. Come spring, I would suggest opening the pool once water temperatures hit 50-55° F. The water will still be cool enough to diminish the likelihood of algae. For now, I would winterize the pool per our recommendations in Pool School.
When you open in the spring, remove any large debris, if any, and then run a full series of tests and note the results. After that, prep your pool for the AA treatment and begin that. If your test results show that your CYA and/or CH (calcium) levels are high enough to necessitate draining some water, the best time to do that is upon completion of the AA treatment. This will remove some of the metals along with some of the CYA and/or CH.