I second that your lips may get a bit numb at the end of a long cold dive, but not to the point of being unable to keep a reg in your mouth.. (unless of course your entire kit viewed in it's entirety were inadequate or an issue like a drysuit flood lead to hypothermia, and in either case a FFM wouldn't help relative to correcting those issues...)
(Side note, purely since you're relatively new to coldwater diving and regs were mentioned: make sure your regs are appropriate for cold water.. to avoid thread-drift a SB search on "cold water regulator" should give you plenty of info and confirmation that your regs are or are not suitable, especially keeping in mind if your 1st stage were breathed off of by you and a dive buddy simultaneously...)