It sounds like the Hearthfire DLC didn't load for some reason. When you turn on the game and it starts, at some point you will see "loading add ons". This is when the game is searching for DLC.
Anyway, here are a few things I would try.
1. Clear your Xbox cache. http://support.xbox.com/en-IN/xbox-360/settings-and-initial-setup/clear-system-cache
2. Clear the game's cache: Hold Left Bumper, Right Bumper and X simultaneously when the game launches and keep them held until the title screen shows up.
3. If you haven't already, install the game to the HDD
4. If those don't help, try deleting and reinstalling the Hearthfire DLC
Maybe someone else will have some other ideas if that doesn't help. Aside from that, it may be better to start with a whole new game.