isn't there a mountain climbing 'bit' called a cramp-on? or is that for ice climing.. (and tree climbing)?

Cramp-on's are worn over your shoes, they have metal points that stick out (on the inside of shoe), and a metal sheild that covers the side of your calf, and that also supports the upper strap that hold the cramp-on on your foot/shoe.

the pointed edge, can be heel kicked into a tree, and allows you to climp up the tree, the same style is used to heel kick into ice when climbing on glaciers.

certainly people have been climbing (and skiing, and farming and herding) in the Alps for ages.. and tools that would help them are nothing new.

i suspect some come from scandinavia, too, people there had to sometimes cross glaciers, or climb on ice .