Won't work because the rainfall won't only happen where the glaciers were, so you would need several dams all the way up and down the rivers.

Won't work, not only because what the other dude said. But also because the alps are getting unstable. The permafrost keeping the mountain tops glued together is slowly melting away, making mud slides and other unpleasant sudden destruction events likelier every year.

If you wanna go ski in the alps do it soon, they will change their looks in the next decade(s).