This action camera is easily mounted on your ski helmet. Apart from shooting video, it can also take 16 MP pictures. The maximum video resolution is 1080p.
From Amazon
Midland H3+ - Full HD Waterproof Action Camera with Wi-Fi for Vlogging, with Stabiliser
Conrad Electronic
Midland H3+ Dashcam Horizontal viewing angle (max.)=120 ° Battery, Wi-Fi
Motorcycleshop.ie
Midland H3+ Action Cam