After I got the Elder Scroll (Dragon), I started heading back to the Throat. However, I couldn't be bothered to run all the way to Ivarstead and then climb the 7000 steps again, so I decided to simply scale the mountain.
Almost there (you can see Paarthurnax waiting if you look closely at the left side of the picture):
Made it! (I arrived right at the bottom of those stairs):
I left Heljarchen at 5am and the latter pic was taken at 6pm, so it took around 10 hours to scale the mountain. I started scaling pretty high up, though, as I had followed the path leading through the mountains for quite a while (starting near the Whiterun SC camp).