There are top bar hives and horizontal hives. I have never kept either, so I am an expert, of course.
I looked at the horizontal hives used in very cold climates, and most of them are very deep hives, which need to use frames to prevent them from becoming box hives. Lazutin hives use 18.5 inch deep frames. in terms of the shape of the hive interior, they are not much different from a double deep Langstroth.
There was a local entrepreneur who was selling a very nice looking and rather pricey top bar hive here in SE Wisconsin, but even he had great difficulty wintering bees in it here. That scared me off of top bar hives.
It is clear that the amount of vertical space between the cluster and the top of the hive determines how strong the chimney effect is, and how much airflow will result, all other things being equal. So when the cluster is near the bottom of a tall hive, they generate more airflow, and as a result lose more heat and consume more food than when the cluster I near the top. This isn't necessarily bad. If they have enough food, they will be fine.
In any wintering situation, you need to have enough food available to the bees to heat them and the air moving through the hive. You also need enough air moving through the hive to carry off the moisture created by the bees consuming the food, which mostly turns it into water. If where you live is very dry and cold in winter (think Siberia, Manitoba, Minnesota) then you need less airflow, as the air is very dry, the parts of the hive are very dry, and because it is cold the bees are using very little of their stores. If you look at how people winter in those locations, they are very concerned with insulation, and restrict airflow as much as possible.
If where you live it is much wetter, and you have long periods of weather in the 35 to 50F range during January, your bees will be consuming lots more food to make brood and comb and forage and take cleansing flights. They will need a lot more air to clear the moisture. The shape of the box has an affect on both airflow and available food, whether there are frames or not. In SE Wisconsin, Ventilation trumps Insulation, so a vertical hive with lots of stores works well.
This also depends to some extent on your bees, as some bees are better adapted to cold weather. None of that is very helpful, of course. If you can find a local beekeeper who is doing it, find out how, and copy them. But don't be afraid to try it. Half the fun of keeping bees is doing it a way that other beekeepers think is impossible.