I haven't visited the area in question, but the South-West corner of England (Devon in particular) has whole villages made of cob, some buildings being hundreds of years old, others still in construction. Cob is their local version of mud and straw building. The region gets a fair share of rain, so the method of building can certainly stand up to bad weather if done correctly.

A TV programme I saw on the subject emphasized a number of points, hope I don't miss any:

Walls are built seriously thick at the bottom and are packed down by the builder trampling the mud and clay together. Higher up the walls are slightly thinner, looked to taper to about 18 inches thick. The whole building ends up as one mass, resembling a cast concrete structure rather than blockwork.

Roofing (usually thatch) extends well beyond the wall so that much of the wall is shaded from direct assault by rain, and any drips fall well clear of the foot of the wall, thus stopping erosion by splash-back.

Some walls have a stone block damp-proof course at the bottom.

All walls are painted over on the outside with lime and whitewash, the regular renewal of this outer layer is the main defence against the elements, but allows the structure to rid itself of damp.