I've just downloaded Hearthfire but as soon as the second logo of loading screen appears, the game crashes. Of course, I've already check mods and launch it without any of them, except Hearthfire : same problem. With all my mods, except Hearthfire : no problem. I've also checked the "cache integrity" and downloaded missing files. But that not resolved the issue. Thank you for your help.
I had exactly the same problem and solved it by letting Steam "Verify integrity of game cache". Maybe you have to do the check more than one time.
The first time I started the check it reported validation failure for HearthFires.bsa and Dawnguard.bsa (in the Steam main folder there is a file "GameValidation.log" with information about the corrupted files detected by the integrity check.)
But then Steam only downloaded HearthFires.bsa again.
Then I started the check a second time: It reported validation failure for Dawnguard.bsa again and then also downloaded this. Afterwards everything worked fine.