At the scout camp I work at in winter, we give scouts two (or one on warm weekends or with a lot of scouts) 1L Nalgenes full of hot water. We put the bottles in their bags, the go on a hike just before bed, and by the time we get back they are roasty-toasty and so are their bags.
I also had a scout with incredibly cold hands and feet a week or so ago. Although I am not sure of the underlying cause (his hands were dry and not frostbitten), a warm water bottle and a sleeping bag kept him fine overnight.
I do not use warm bottles at camp, and have not been out in winter outside of camp in temps where they might be necessary. My winter hydration system is a 1.5L Nalgene bladder, which has a wide-enough lid to easily pour hot water into. I am taking my girlfriend winter camping in two weeks, and depending on conditions, a hot water bottle for her is always an option.
Other options for warming up extremities include putting on boot liners, wearing dry, loose socks, drinking water, eating some food and urinating, etc.