I've often wondered about this. Clearly, pool chemistry does not remain stable during the winter months after pool closing. The chlorine breaks down and I've often seen the alkalinity drop significantly as the dissolved carbon dioxide outgasses from the water over time. The pH drops as well, mainly due to acidic rain/snow as well as the reduced buffering ability from lower alkalinity.
How often is it recommended that the pool water be tested and adjusted during winter and early spring, especially once temps rise about 50F and the algae awakens from its winter slumber?