Okay, so this may sound like a stupid question, but I want to be 100% sure on this. Are snow-covered lands an exception to get from fetch lands? For example: I play a Bloodstained Mire and use its effect to search for a land when all I have are snow-covered lands (well, in reality half my basic lands are snow-covered but I just want them because they look cool). Will that be an exception to the whole "search for a swamp or mountain card" rule?

If the card says "snow-covered swamp" or "snow-covered mountain", it still says has the type "swamp" or "mountain" and so would be a legal card to fetch.

Okay thanks. Just wanted to double check.

Yes, it's legal. Fetch lands can also fetch Shocklands