Skin is the outermost layer of human body, and is in direct contact with sun. Of course, many skin conditions are influenced by UV rays. Sometimes, even acute cold too makes skin crust break away. From this analysis, it is easy to bracket countries that are most-prone to skin diseases.
Tropical countries (especially in Africa e.g. Somalia) suffer a lot. Heat there is oppressive and people aren’t quite knowledgeable regarding sanitation. Laborious lives of mainly poor population in the Dark Continent are another reason for spurt of such diseases.
Places in UK are inhabited by people with freckles and sunburns. These however cannot officially be categorized as skin diseases. Cold countries like Russia and Norway have their own acute skin problems.
It is noteworthy that diseases like scabies, herpex and eczema are not related to weather phenomenon. These are largely hygiene-based. Often, small blisters grow into space and culminate into a sizeable disease.