I can usually keep them alive over the winter, so I'm pretty sure this is correct. There are a few things to consider here.
One is that even as spindly as yours is, it's a big plant and the pot looks too small. The pot itself looks like a typical decorative plastic pot with tiny holes in the bottom to which expanding plastic clips on its saucer hook onto, blocking most of the drainage.
I fear that even though you are trying to be careful, this pot and possibly the soilmix conspired to drown the roots. Poinsettia is SERIOUSLY drought tolerant. You really shouldn't need to water more than once a week especially during the winter when they are semi-dormant.
That brings me to temperature. It's actually better to keep them on the cool side during winter -- I have one plant on the floor of "Cool and Gang" area which is furthest from the thermostat and is least heated. (But when the heat turns on, the floor level vent which is blocked by a storage unit directs the heated air sideways to where the plants are. I have another, smaller one in a SE window very close to the windowsill but not on it. (The smaller one is a cutting that rooted from pruned branches of the bigger one
When I had the big plant upstairs last winter, it lost most of its leaves.
Now this is the tricky part. Are you "attached" to the those curled branches? -- my recommendation is to cut back most of those branches except the new shoot from the bottom. It's a little scary I know, but if you cut back to just above where the bark is grey and last year's new growths where the stem is still green (about an inch above the gray, leaving some greenwood at top), I guarantee those will grow new buds and leaves.
It's a little harder to say if they will grow back when cut back to the old wood with gray bark, but mine did -- just not all of them. Some of them dried up and died.
Picture it bushing out from the cut stems into a nice compact plant. I think this will mean cutting off all of the meandering stems to where they are more sturdy and upright.
Even though it's middle of the winter and the plant is stressed, I would still take the plant out of this container and put it in a pot with good drainage holes about twice as big. Shake off the existing soil mix and add 2 parts potting mix and 1 part sand, and blend them all together to use for uppotting.
I realize this is kind of contrary to most recommendations not to repot when stressed. Alternatively, you could leave it in this pot and cut back to once a week or less watering, and uppot later when it stats to grow again. (But I prefer not to disturb it when new growth starts because the new buds are usually being supplied by new roots.)
For now, I would put it near a bright unobstructed window -- SE, S, or SW facing. It doesn't have to get the brightest light while dormant. Temperature should be around low to mid-60's. Keep it on the dry side, giving about 1 cup when you water. Be sure to thoroughly mist at least twice a week.
Some of my "tropicals" and "sub tropicals" are starting to wake up and grow new shoots. It may take a little while longer for your location further north, but I think the longer daylight hours are triggering them. I have to cut back my poinsettias (by about 1/3 to 1/2) before they start growing. (When they start to grow, there will be LOTS of new buds and shoots.)
Once they start growing and leaf out, they need to be watered more often and more volume at each watering.