How important are climate and erosion in explaining how mountain belts are formed? Why?

Not much. The formation of most mountain ranges is caused by either plate tectonics or by glacial buildup. Climate and erosion explain why mountain belts are (very!) slowly earing down and disappearing in parts. The Appalacian mountains are a very old mountain range and scientists estimate they used to be much taller but have eroded down to where they are now.