For a log house, hip, half-hip, hipped, multi-gable, single-pitched, double-pitched, vaulted, diamond, and flat roof shapes are suitable.
I will tell you more about the double-pitched and flat roofs.
The first is the most popular in Russia. Any type of roofing will do for it. It also allows you to increase the living space of the house due to the attic and provides young families with the opportunity to increase their living space in the future without large investments. But for this, you need to provide independent floor joists on the roof and a place for the opening of the flight of stairs in advance.
Wide eaves and gable overhangs give the roof and house an aesthetic look and additionally protect the walls from precipitation. They are made by extending the rafter legs beyond the outer walls along the length of the house, as well as false rafters from the gables.
In a large house with a first floor area of 90 m² or more, overhangs of 1 m or more are well perceived – this is after the exterior finishing of the walls.
Flat roofing has become popular in recent years, as it is economically justified due to available materials and the cost of installation work compared to other types of roofs. In fact, there is a slope, but it is minimal. Snow that accumulates on the surface is an excellent heat insulator, it can serve as temporary insulation for the roof during the winter.
If the outside air temperature is -25 … 28 ° C, and the height of the snowdrifts is from 25 to 30 cm, then the soil temperature does not fall below -10 ° C. This means that the temperature on the roof surface will also be -10 ° C.
But to calculate snow or other loads, for example, if a terrace is planned on the roof, you should contact the designers.