Not everyone plays the same role. I personally love the premise of High King of Skyrim, which is lore-unfriendly as hell, and my main criticism is not the incompatibility with lore, but the general lack of polish and game-breaking nature of some of the commands.
There are other temperate areas in Skyrim. Parts of the Rift and Eastmarch - particularly the hot springs - are also rather suitable, and Cloaks of Skyrim provides you with something warm for the in-between places like the Whiterun or Falkreath holds. Journeying north of Windhelm without winter clothing seems like a terrible idea for, say, a non-magical Imperial, though.
As for armor, there are many character builds that would not need much of an armor. Mage classes usually wear unarmored robes and combine them with wards or skin toughening spells, and a skyclad mage deriving power from an increased connection with nature, rather than an enchanted robe, does not seem that far-fetched. Players who are not magically inclined might focus on speed and ranged combat and/or hit-and-run strategies. It still takes a lot of courage to go into battle without armor, but again, Beowulf may be a mythological inspiration there.