Do you have a cold cellar. You can overwinter pots in a cold cellar that is just above freezing. Let them dry a bit so they are just a little damp and cut back the foliage to about 6 inches removing all the flower buds. Then stick them in there and forget about them until spring.

In spring about a month before you want to set them out, take them out of the cold cellar and put them where they get indirect light. Give them a little water--just a bit. Gradually give them more water and light until they start to show new growth and have full sun and water.

If you don't have a cold cellar then yes trim them back again remove all the flower buds, and tip them out of the pot. Don't touch the main root but you can remove some of the feeder roots. Give them the biggest pot you can and pot them up. I do not allow mine to flower all winter.

You can also take cuttings. I do this every spring, but if you want smaller pots it might be the way to go now. You could have a sizable plant by spring. Don't allow them to flower and they'll put on the best growth. Here's how to take cuttings

TAKING GERANIUM CUTTINGS
First you must make sure everything you use is very clean.
Take your cuttings: With a sharp knife or razor blade cut a 4 or 5 inch piece from the growing tip, cutting just below a leaf. All roots and branches come from a leaf joint. Remove all but the top 3 or 4 leaves. Let your cuttings callus over--Lay them out somewhere on newspaper. A piece of masking tape beside them tells the color. Mine sit on my spare room floor. Let them sit for about 5 days. The leaves will look wilted and dead but they're not. The cut end will shrivel and dry. Letting them callus over and watching the water cuts down on blackleg a deadly fungal disease especially to cuttings.
Now plant your cuttings. In a clean pail mix your soil with the water so you make sure the soil is damp right through. Use a soilless mix like pro mix or one that is formulated for seeds and cuttings. Just make sure it has no fertilizer in it. You want the soil wet but not too wet. Squeeze a handful and some moisture should come out but not a lot. Fill your pots and make a little hole in the center with your finger or something else that will make a small hole.
Dip about 1/2 inch of the cut end in rooting hormone. It comes in powder or gel, either is OK as long as it's for soft wood cuttings. I use Stim-root NO. 1. After it's dipped put it in the hole and cover it in, and you're done.
Keep the soil moist but not overly wet. They will look wilted at first but that will change as it starts to grow roots. You will know it's rooted when it starts to show new growth. If you are going to plant it outside, wait until it is rooted well before you set it out.

If you wanted to keep them in a cool place and let them be until March, the above might work but if you wish to keep them going, flowering as best you can keep them, then what you think to do.....do it. Divide the plant. The amount of root ball you end up with might not be sufficient for the amount of foliage/bloom that you hope for....in such cases, cut back the amount and let the root ball feed the rest in a proper way.
Fresh potting soil or soiless mix is put into a pot that drains well. Put some gravel or small shards of clay into the bottom of the pot, then the fresh soil. Make a hole in the center and place your divided plant in, firm up, water well to drainage. Let the plant drain fully before you put it into a sunny window. Do though keep regard for the amount of sun coming through the window glass because, even October's sun, can burn. Turn the plant about every other day to ensure all parts get equal sun and place it closer to the window as the sun intensity dwindles toward December 21. Then think to pull back the other way as the sun comes back north.

When you water, always water to drainage, and dump the excess and let the soil dry down some between waterings. If the plant seems to be growing well, then a little, very little, fertilizer can be given...dependent on the amount of foliage/bloom.

The sunlight you give it will determine how long the plant might continue to bloom. Even if it stops, keep it going like any other houseplant. Maybe it will produce more.
It will likely get lanky....the low light levels might not be enough. You can give consideration in March to cut the plants back severely and start all over, remove all foliage, old stems, bloom if any, consider fresh potting soil and begin again their re-birth. In about 2 weeks given good sun, they'll begin to produce new foliage and gain more as the weeks go by. Put outside when the chance of all frost is passed.

If you have a cellar just leave them alone and place them in front of the windows where the'll be quite cintent untill spring. My wife has been doing this for years. I might add that they are in hanging baskets and she does cut them back a bit. Happy winter.

Geraniums as house plants. I bought four small zonal geraniums this fall. I couldn't resist their lovely colors. They are small enough that I keep them on the window above my sink. They have bloomed all winter. I don't think they like too much water though. I almost killed my best one by watering it too much. They are all four doing great, and they brighten up my kitchen window, here in the winter.