I'm in climate zone 5A under the 2015 Model Energy Code and International Residential Code. The requirements for this zone are R-20 for the walls, R-49 for the ceiling, and R-30 for the floor. I just don't see how anything like a log cabin can come close to meeting that. They would be great for a camp cabin that doesn't qualify as a permanent residence, but they couldn't be built as a primary residence in this climate. Farther north, it gets worse. In zone 6 the requirements jump to R-20+5 or R-13+10 for walls, R-49 for the ceiling, and R-30 for the floor.
Those are for frame walls. There's a separate column for mass walls, which is what a log cabin would be
IF the wall weighs at least 20 pounds-per-square-foot. For zone 5, mass walls require "13/17," which means (and I'll quote):
“15/19” means R-15 continuous insulation on the interior or exterior of the home or R-19 cavity insulation at the interior of the basement wall. "15/19” shall be permitted to be met with R-13 cavity insulation on the interior of the basement wall plus R-5 continuous insulation on the interior or exterior of the home. “10/13” means R-10 continuous insulation on the interior or exterior of the home or R-13 cavity insulation at the interior of the basement wall.
So you can't build a log cabin and leave the logs exposed on both the interior and the exterior.
Zone 6 for mass walls is R-15/20. Northern Michigan and northern Minnesota get into zone 7.