When I lived in Columbus, OH, I guess winter was that long, mid-Oct. to about mid-April. I'd blocked those horrible memories it took years of therapy to get past until you dredged them back up! But, while the horror is still fresh in my memory again, yes, you can keep cuttings of PS in water. Always put mine on a windowsill, had N & S windows at the last place, so can't speak to any method/light situation besides that. Also did Coleus there the same way.
Coleus needs more light during winter than you might think. Even down here, they like being in a south, east, or west window, but not so much in a north one. PS doesn't seem to care which window. Also had great success keeping Perilla 'Magilla' in water, and one year, some kind of tall red Alternanthera. Almost any flowering 'annual' plant wintering inside would like as much sun as possible. The rays in winter are much weaker, and of shorter duration, so any kind of sunburn is unlikely (even on a shade plant) that's been outside for summer. I'd love to know if anyone has managed to do that with something. I'm famous for sunburning any kind of potted plant, but have only managed to do it to 'house plants' so far.
There are anecdotes of many other kinds of plants surviving winter as a cutting in water. If it's just going to be turned to mush by frost and you have the space, worth a try (for true tender perennials, not real annuals) IMO. Stuff that's easy to grow from seed, I wouldn't spend indoor space on, but some might want to try to have "a huge one" next year, so might negate the seed-ease thing for them. Coleus does grow easily from seed, but the only seeds I ever see are rainbow and wizard.
In general, long-term water cuttings... a jar with a large opening is best, the roots can fill a bottle and be impossible to remove from one shaped like a coke bottle. Don't forget to check if they need water. Rinse roots, container, and replace water if it gets any kind of color or scent. Otherwise, I don't change water, there's way too many of them for that. No leaves under the water, they will just rot. If debris falls in there (Coleus will keep making flowers after it's made some roots, discard a leaf occasionally,) it will sour the water, maybe float on top and get moldy, so keep an eye out for that so you can get it out of there if something falls in.
Potted plants give a lot more options for overwintering. Wax Begonia is one of my favorites, keeps blooming & growing all winter. Aptenia and (many) Plectranthus are common house plants, so absolutely worth overwintering attempt. Either of these can be snipped and stuck in a pot next to some other plant to hitch-hike inside for winter if desired, or given pots. At the "wrong time of year" for propagation, I have a lot better luck sticking cuttings in existing pots vs. new pots with no existing roots to dry the soil regularly.
Datura survived coming in potted last winter, and several cane Begonias. Tahitian bridal veil (Gibasis geniculata,) any Tradescantia, Pelargonium (zonal Geranium,) so many other pretties can be saved.
After seeing Marquest's beautiful potted plant that lounged in her basement for winter, I would turn to her for winter care for a potted plant. I've never killed one bringing it inside, but have also never had a good looking plant to put back outside in spring. The leaves all fall off except for a few at the tips. I've tried putting them in great light and had the same results so last winter, I only kept one, on top of the microwave, and let other plants have the 'good spots.' There's a window next to that, but it faces north and a porch roof is over it, so it's light, but never direct except maybe a few minutes right before sunset.
This is my favorite thing in gardening at all, overwintering. So much that I've completely disregarded the 'rules' for plants and am using house plants as annuals, insisting that tender annuals perform perennially, hardly have any real perennials 'cuz most of them only put on a show for a few weeks and just seem to be 'in the way' of prettier plants. I buy with an overwintering eye. If it's an annual that can't be saved, I'll probably pass for something I can, unless it's a really good nectar plant for butterflies and humming birds. The 'flower beds' are full of tropical plants (mostly just foliage,) and anything that will make nectar. It's what makes me happy. People walking by say, "I love your flowers" but there are hardly any. I'm still going to spend my 'garden money' every year, but I like for it to go to something new, not the same old stuff. Eventually I'd like to reach the point where I say to myself, "All I need this year is some prettier pots," or even get into some bigger, more expensive stuff like shrubs or fruit trees, hardscape items. With such a small house and no basement, I'm not too hard on myself for 'needing' new plants instead.
This year, I'm going to attempt to keep Pentas, and Heliotrope, both to be potted once rooted, though never did a cutting of the last, will see. Angelonia is not a true annual, I'm wondering about that also. Any anecdotes on these?
Polemonium was (supposedly) perennial when I had some in OH. It did come back the next year, then I moved, so really don't know much about that plant. The variegated leaves were why I got it. Hardly any of the plants I have have plain green leaves, unless they are of an unusual shape like heart-leaf Philo.
What else are people saving? Enable, enable...
These were better last year, when July actually had some sun!
House plant or annual (tender perennial?) The lines are blurred here!
Let your imagination run wild! This spring, this pot was just Thanksgiving cactus. Will all of these plants stay alive in side this winter? IDK, but would bet on "most."