Digital Video/Still Cameras on the mountain

I have a Sony DCR-PC9 miniDV camcorder that I use for video while
snowboarding. Here is my problem, the LCD barely works while on the
hill, I can only see slight shadows like images in the LCD or the view
finder. I am thinking its related to the cold. How can I get around
this? Makes taking video a wee bit difficult. I still get some
shots, but its not easy. I keep it in a case, in my jacket until I am
ready to shoot, but its still does not solve the problem. Also,
pretty much as soon as I take out my camera, it starts flashing that
my battery is dead.

The battery problem also happens with my canon digital elph still
camera, but I think that might be due to the body being metal, and it
gets ice cold instantly.

Anybody have these problems? Is there anything I can do?

Thanks,
-flynn