You don't see flat roofed houses much except in places like New Mexico, Arizona and California. Why?

 You don't want a flat roof if it snows much where you are. However, the exception to this is likely New Mexico where it might snow in places like Santa Fe a lot but there are still quite I few flat roofed houses there. A Flat roof is okay only if the drains don't clog that relieve the rains and keep them from turning the roof of the home into a lake where the roof eventually will collapse like it often will from too much snow load too. For example, if you get over 6 feet of snow on most roofs they might start collapsing in those dwellings. If you get over 1 to 2 feet of water on your flat roof and it cannot drain it may or may not collapse but strange things start to happen like water coming out of your interior walls which is what happened to my girlfriends house in 1995 when the rains were literally biblical sort of like Noah's Ark rains or something like that. Then I got barefoot and went up my girlfriends aluminum ladder which reached the top edge of the roof. Then I cleared the leaves which were blocking the roof drains. Later that week I bought something similar to chicken wire so if more leaves gathered I had made boxes of chicken wire like wire about 2 feet by two feet square which would stop the leaves from clogging the roof drains in the future. I got this from one of the Ace Hardware stores nearby my now present wife's home then on the northern California coast.

If you live in a heavy snow area one solution in a mountain cabin is to build and A-Frame like I did in 1980 on the side of Mount Shasta. Then whether you are there all the time or not you don't have to shovel snow to prevent roof collapse because the angle of the roof is enough to shed any snow that falls enough to prevent your roof collapsing from snow load. So, the most extreme slope for dealing with snow load is an A-Frame and the other extreme is a flat roof or dome. However, I haven't lived in a dome shape even though I have spent the night in a few my friends owned and built. But, I also have spent nights in 1 and 2 story teepees which also shed snow very well too sort of like an A-Frame. But this was mostly in Mt. Shasta in the 1970s and 1980s.