Geraniums are easy to propagate. Cuttings can be taken at any time. They can be water or soil rooted: medium can be moist sand, or a rich potting soil cut with some extra vermiculite for drainage.
I find my plants get huge and rangy over the winter because I don't have enough 'large space" light for large containers, so I take cuttings in fall. The cuttings go into rooting medium in a shady outdoor space and are kept moist. By early October they are ready to be potted in 4" pots and brought inside and into the window for winter. I grow them like a houseplant in the Southerly windows all winter and just keep some pretty pots on hand for them to be showy in. By spring they are a good size (easily fit into a large 5.5" pot) and ready for going outside. Zonal geraniums don't do as well for me inside, and I don't grow them at home. We found at the store I worked in that they need better drainage and much more light and warmth. My "regular" geraniums are kept all winter at 58 degrees (or slightly warmer) - a barely heated house but in the window
I over winter before frost. Geraniums are not frost tolerant.

Thank you GGG. Your information is really helpful. I'd read of others overwintering plants on the windowsill. I don't have much window space so I'll have to find another solution. I'd like to take 20 - 30 small cuttings and have plants ready to go out in the spring.

If I keep the large plants indoors, alive and watered in my cool basement, will they survive until Spring? If so, maybe I can take cuttings in February, grow them out, then plant outdoors in March/April.

The plants will live but will look pretty wrangy unless you have some very bright lights. My mom lives up north and overwinters her geraniums in a cool room with loads of sun from two windows. They do pretty well.
The other option is the old shop lights option. You can also be creative about window spaces for plants. We put narrow shelves across the middle of our windows, just big enough for some small pots. Great for cuttings.

Shop lights - yuck! They bring visions of white flies. Thanks GGG. I appreciate your help.