That was one question I had …
Looking around, it seems that some places have cabins with walls just 28mm (just over an inch) thick – others, more than 150mm. Now I’m no expert in construction techniques, but I’m sure that within reason thicker walls are better. I’m not building a nuclear bunker – so 6ft of lead-lined concrete buried 10m below the surface is probably overkill (although I expect that very little sound will escape into/from the environment).
Although it is cold and wet today, here in the UK we don’t have an extreme climate – at worst we are a few degrees Celsius bleow freezing, and don’t get much above 30 in the height of summer. (It has been said that the UK has “weather”, whereas other places have “climate”).
Anyway to cut a long story to size – I found a place that supplied cabins with 110mm timbers (about 4″) – a reasonable compromise. The “logs” themselves are about 110x160mm and the logs sit on top of each other jointed by a tongue-and-groove arrangement (5 tongues) which seems to make a reasonably draughtproof joint. (See a picture of the logs)