Before you go to the smith - lets try something simple. If you don't have any, go to any auto parts store or Walmart and get a can of degreaser or carb. cleaner. Remove the bolt from the rifle. If you don't know how to disassemble the bolt here is the link (go to page 14)
http://www.remington.com/pdfs/om/om_7700710.pdf
Once disassembled, spray it down with the degreaser/cleaner and wipe dry. Lightly oil with Remoil or some other quality gun oil and reassemble.
My suspicion is that you bolt is freezing up a little in the cold but not enough to lock it up completely. Your first shot 'breaks the ice' so to speak and allows the firing pin to move freely on sucessive shots.