Maille and plate are the only two of those that were used in the entirety of western Europe (the only area I know anything about so I'll stay there for the most part) in the middle ages and both were used from the frosty tips of Scandinavia all the way down to the southern tip of Spain. People just used what was the best armour they could afford. Armour was hot, be it maille, plate, lamellar or cloth (probably the most common type of armour, clothes are quite cut resistant and a good gambeson is largely arrow proof), so you'd usually only wear it when you needed to. War was more of a summer sport as its hard to feed and move an army in winter, so cold wasn't usually a huge factor. Heat on the other hand, was. One theory as to why the French lost the battle of Azincourt was that while they were stuck in the mud with their visors down (to protect from the arrows) they suffered from heat stroke, killing some outright and weakening many more.