I have the same problem. Opening a save in Skyhold, then going to the Deep Roads through the War Room or through the Storm Coast causes the game to freeze. There is no way to continue to Deep Roads. I have played this game for many years, on several different computers, and this has always been a problem. I usually don't even bother. I have always played as a male. This game I am playing as a female elf, so I wanted to take her to the Deep Roads. This should have been fixed and patched by now!
NOTE: I was able to use a work around. First I saved the game right before going to the Deep Roads. Remember the version number in the file named "package.mft" located in the folder "Dragon Age Inquisition\Update\Patch_ModManagerMerge". Using that number, change it in file with the same name in the folder "Update\Patch". Then cut the whole "Patch_ModManagerMerge" folder and paste it somewhere safe, so you can put it back when your done. If you don't change the number, when you load the game again, you will get the error "The Save Data Was Created With a Newer Version of the Game. Please Download The Latest Patch and Try Again."
After you go to the Deep Roads, save your game again and exit the game. Then change the version number back in "package.mft" in the Patch folder and move the "Patch_ModManagerMerge" back to the Update folder or you can merge it again if you wish. You should be able to load the game and continue to play it.