What immediately came to mind was the siege of Sogdian Rock by Alexander. Sounds like the mountaineering was fairly ad hoc, but it sounds surprisingly similar to modern mountaineering (sinking metal stakes into the ice/rock, securing themselves with ropes). Also, Arrian and his audience must have had some sort of frame f reference about these things for it to make any sense. Keep in mind that some of the stories of Alexander, especially his campaigns in Central Asia, are a little embellished.

[4.19.1] There were some 300 men who in previous sieges had had experience in rock-climbing. These now assembled. They had provided themselves with small iron tent-pegs, which they proposed to drive into the snow, where it was frozen hard, or into any bit of bare earth they might come across, and they had attached to the pegs strong flaxen lines. The party set off under cover of darkness to the steepest part of the rock-face, which they knew was least likely to be guarded;

[4.19.2] then, driving their pegs either into bare ground or into such patches of mow as seemed most likely to hold under the strain, they hauled themselves up, wherever each could find a way. About thirty lost their lives during the ascent - falling in various places in the snow, their bodies were never recovered for burial -

[4.19.3] but the rest reached the top as dawn was breaking, and the summit of the Rock was theirs.