I just downloaded Hearthfire, and I noticed a strange glitch as I load my character. All of the children in my game are running around in their underwear. I have yet to try to buy land, so I do not know if the DLC itself is broken, but the children are annoying. Any help would be appreciated.

Have you downloaded the right language version DLC for your game? Did you restart the game after downloading the DLC. Perhaps try restarting the console and see if it finds what is missing.

I downloaded the only version there was. I deleted it and all of the children regained their clothes, I will try to download it again.

Which does not answer the question, DLC does not support imported games, was it the same language version as your main game?