Cold weather problems

I have a new Motorola Droid w/Verizon. Below 40F, my fingers will no longer operate the screen. Last night at 21F, I got a call that went directly to voice mail and when tried to check voicemail, the phone froze completely. I tried to restart it... it came up with "call in progress" when I tried to check voicemail. After about 15 minutes inside, the phone started working again normally. Is this a problem with all Droids or do I need to get another phone?