When I was younger and had summers off from college teaching, I toured in the alps four summers in a row. I trained for the trip by running stair laps at our local football stadium all winter long; indoors when the weather was bitter cold or snowy.
The real benefit was the aerobic stuff...I ended up with lung capacity 40-50% larger than average. I remember climbing in Switzerland and could see my breath in the cool mountain air, and how low my breaths were per minute, even on the alpine passes. My appetite was phenomenal.