Good advice MT

You should always breath in thru nose and exhale thru mouth on exertion. I know people with sinus issues or nasal obstructions can't always do this, but it's the best way to keep the O2 flowing and the lactic acid from pooling so fast when your really working hard.

Most people unless their into working out, especially cardio activity, breath thru the mouths. If you are a mouth breather and you want to boost your cardio ability, learning to breath properly is a simple step that will pay big dividends down the road.

If your new to the practice, it helps to " exaggerate" the exhale thru the mouth, but once it becomes routine, the exaggerated forceful exhale should stop, as it actually saps energy especially if your doing it out of rhythm with your natural breathing pattern.

The mountaineering cadence is great as well. I'm sure MT would agree, standing as upright as possible when going up grades is important as well. You see a lot of people hunched over under the load and taking little shuffling steps.

Hunched over, your compressing your lungs, restricting the amount of air you can inhale. Your also straining your lower back, becasue the weight isn't over your hips and directed vertically on your spine/hip area.
Instead of little short shuffling steps, try thinking about lifting your knee, extending your leg and then stepping forward while maintaining proper posture. You'll find it much easier to breath, easier on your neck/shoulder areas and surprisingly you'll be able to climb with less expended energy and much quicker than being bent over ;)