Just to give you an idea what to expect in colder weather with less sun: My pool stays open all year, even though it's too cold to actually swim. But my Aussie SWG is designed to run all year. Over the peak winter months, my pool doesn't get any direct sun. I maintain FC around 10ppm over winter, with daily losses of about 0.25ppm per day (or about 1ppm in four days). I just set my SWG to produce 0.25ppm per day and that keeps FC pretty stable. In July (equivalent to your January) I was away for four weeks and just bumped up FC to above 20ppm, and turned everything off. When I got back, FC was around 9ppm, pretty much what I expected (When calculating losses over a longer period, you have to consider that the daily loss is not a fixed number, but relative to the FC-level. In my case I actually lose 2.5% per day in winter, which means 0.5ppm at 20ppm or 0.25ppm at 10ppm. The calculation would be 0.97530=0.47 - over 30 days FC will get reduced by a bit more than 50% with daily losses of 2.5% (or 97.5% surviving each day)).
Once the sun starts hitting the pool again and the water gets warmer in spring, I have to ramp the SWG up again.
In your case, the SWG will probably shut down at some point, and you'll have to switch to liquid chlorine.