Welcome to TFP!!!
In our climate, we do not really close the pool. It just gets too cold to want to swim in it. You still need to maintain the chemistry just like you would in the summer, although the chlorine loss is much less in the winter.
Regarding the "typical amount of maintenance", it depends. If you spend enough time on the forum learning, most members spend less than 5 minutes per day to maintain the chemistry. Then you will also need to clean the pool as required (depends on your debris load).
The TFPC method we teach is really just about understanding your pool’s chemistry and through accurate testing, adding only what the pool NEEDS and not what someone wants to sell you.
I suggest you take a look at the articles in
Pool School starting with these:
ABCs of Water Chemistry
Recommended Pool Chemicals
How to Chlorinate Your Pool