Just out of sheer perversity (and impatience to get what was on the top), I tried climbing the Throat of the World before going to High Hrothgar. I tried scaling the north side first but met with an impasse (either direction I would go would take me to an area steep enough that I'd fall and die), so I thought I'd take the steps but was too tempted and tried it again from the south. It took me about 2 hours but it was doable. I never thought doing such a dull and tedious task would be so exciting

Especially as I was getting close to the top and could see my goal but wasn't sure if I'd get myself stuck in another death-trap.
No one was home at the later quest-destination.