Tbere is never any advantage to rooting anything in water that is not a bog or underwater plant. Never. Do what you said, and be sure not to let the potting mix dry out until new growth appears. Then you will know they have rooted, and you can cut back on the watering.
If you haeve to prune them mid-winter (you have LONG winters) you can also root those cuttings. Why not just use 4 inch pots? Easy to manage.
If tubers (potatoes) have formed, it would be easier to dig and store those in a cool place until late spring.
You probably know this, but give them as much light as possible. Even then, they are going to get very leggy indoors.

I just saw a guy on TV doing cuttings of sweet potato vine. He said not to use the end of the vine, but instead a short section in the middle of a vine with two leaves close together.
Have you seen the variegated one?

That's interesting. I know the tip has the most growth hormone. That's why you cut it off to induce side branching. Maybe, by not using the tip, you induce better rooting. I've got a bunch stuck in a pot (with tips) but they are still wilted-looking after a week. It's been so cold though, maybe they don't want to root.

I did get some varigated ones too. I planted them in a hanging basket.

I've rooted 'Blackie' and 'Marguerite' (the chartreuse one) in water and in soil, and carried over winter in whichever medium I started with. Just place near window or actually on windowsill here is fine...doesn't get too cold here even if leaves touch window. They occasionally get a yellow leaf or two...I just remove.

Crocosmia, thank you for that info re not using tip cuttings...interesting as the tip cuttings work so well on all types of vines plus other plants. In fact I have Manettia inflata and Dolichos lablab tip-cuttings in water in kitchen window, continuing to produce blooms and in the case of the lablab, tiny purple pods. I've still got lots of Marguerite outside so I'm going to try a few experiments...lol...will report back...stay tuned.

I might mention too that I prefer 8 to 12-inch cuttings in water. In fact I usually just make a nice arrangement of some of my larger Coleus and add the sweet potato vines. All usually root with no problem. I'm wondering now if the longer cutting with sturdier stem helps in rooting..those tips are so wimpy sometimes.

Eldo, actually I find the advantage of rooting in water is that I can save far more tender plants over winter...Coleus and Alternanthea and Cordyline or Ti (the so-called 'spike plant' in red or green)...plus Croton and the tender Hibiscus 'Jungle Red', etc. So-o-o much easier to keep bottle/jar topped with water than carrying over in pots. BUT ...and here's the key: in spring I just take cuttings of the tops of the water-rooted plants, and start those cuttings in soil. I throw away the mass of "water-roots". To be honest, I started this when I found it impossible to get the water-roots out of tall thin bottles so now I just cut off the plant top and throw bottles away...LOL

The variegated type was glacially slow-growing for me and also the leaves curled in a strange way...maybe some sort of disease? I tossed it. Anyway, I've noticed the few I've since seen for sale don't look too healthy. Maybe there are several variegated selections and I've just had bad luck. I've seen another black one, with heart or spade shaped leaves, and one with bronze leaves somewhere on line.

Didn't mean to run on so...just feeling good because I finally got all my tropical houseplants in for the winter and found space for them again...of course now we can't see out of windows...LOL josh

Anyone want to give an update? Did you successfully root your sweet potato cuttings? I took cuttings last fall but hardly any of them survived. My whole plants, however, wintered over mostly very successfully, but are now quite leggy and long. I had several variegated ones and all but one died. The black and chartruese are healthy. This year the price seems to be way up to buy them and I'd really like to use mine.

I overwintered mine in water and they did great -- except when I accidentally let the water get too low. So, I cut the stems off from the dead roots and the vine quickly made new water-roots. I read a posting from Al about making the transfer from water to soil and tried his method. ... It worked ... sort of ... the cutting was on the verge of breathing its last when it finally just "took." I watered it every day and kept it in the shade, as Al suggested. He also suggested covering the pot with plastic, which I did, but I think the poor thing nearly cooked. The vine looks great now and is growing on its own. I still have a piece inside the house in water. I may just leave it there.

Here is a link that might be useful: Al's advice on taking roots from water to soil -- see last entry in thread