An aerobic exercise is one that uses the oxygen (hence 'aero') that you're taking in as you breathe, while anaerobic exercise is that which uses the oxygen already stored in the muscles.
Hiking is steady and relatively low-intensity (aerobic), while a 100 m. sprint would be anaerobic.
I don't know about you, but when I'm hiking I usually walk with a long stride, using not much of my quads, so I don't see how that would be a good conditioning exercise for skiing. Same with running - it's aerobic if you do if for more than a few hundred metres, but the muscles are different. There are people who train for hiking by climbing stairs, but in my experience all that does is cause repetitive stress injuries from doing exactly the same movement many times.
Squats in the gym would be a good way to build strength in your quads. Then add weight and reps.
go faster. It pains me to see people trying to go slow and working so hard...
you can also go sideways down if its icy/steep. keep your skies together and turn your hips 45degrees to the slope ( your shoulders are always square to the slope right? ). This can be harder on the hips but you can switch it up and your more ready to stop if needed to rest.