ACROSS
3. A person who climbs mountains, a mountain climber → mountaineer

4. Illness caused by ascent to high altitude, characterized by hyperventilation, nausea, and exhaustion resulting from shortage of oxygen → altitude sickness

5. The pointed top of a mountain → peak

6. A camp from which mountaineering expeditions set out → base camp

7. A tool consisting of a shaft, grip, strap, etc., used to reduce the burden on the lower body and maintain balance when climbing→
  stick

DOWN
1. A covering for the hand that has separate parts for each finger →
          glove

2. A type of flashlight/equipment designed to be worn on the head and fixed to the head →  headlantern

3. A building located at high elevation, in mountainous terrain, generally accessible only on foot, intended to provide food and shelter for mountaineers, climbers and hikers → mountainhut

8. A set of outdoor activities that involves ascending mountains →          climbing