Without stairs?

(i could not fit this all in the title)

No. You must climb the 7,000 steps to get to High Hrothgar and then travel on to the summit.

http://www.uesp.net/wiki/Skyrim:Throat_of_the_World

Never done it myself, but apparently it can be done.

It can be done. Ive done it myself with no horse. It takes a while as you sometimes have to circle 359 degrees (Not 360...) to find that one spot you can jump from to get up to the next "level". Its just a lot of circling around the slope looking for anything you can use to get up higher, be it a lower grade incline, or messing with the physics and wedging yourself between rocks.

Yep, I usually try to get that special pickaxe ASAP It takes a while but it can be done.

Either use a horse or you mountain climb up at certain spots.

Indeed it is possible. It takes a lot of patience but I found out the hard way... that damn storm will kill your ass.

Tcl

I have done it several times, first character I never realised what he was climbing, third character started climbing the stairs way back around level 9, could not win a fight and took to the hills to avoid a sabrecat, got a nice pickaxe out of it before I eventually worked out how to drop in on the grey beards roof. First character was no where near the stairs, he did it the hard way, neither used a horse.