How does world of warcraft's environment work?

if i downloaded wrath of the lich king, but the game was set in cataclysm, would the place be snowy, and people talk about the lich king? or would it be warm, and look like anyone else's thing? and how do quests work for dlc? where do you start em, and is it like a direct storyline? or do you just have to explore, and find the guy who gives you the next quest?