the one you're talking about with the huge dude kidnapping a little girl and then ripping her doll in half (and later batman tracks the girl down to help her get over the childhood shock) is in Volume 1, (the particular story is "In Dreams" by Liberatore and Helfer).
It snows in a lot of the stories, but you could be talking about the very excellent Bill Sienkiewicz story in the same volume (a dad throws his son's kitten off a rooftop, Batman isn't sure how to proceed at the risk of destroying the son's life)... that or the Kristiansen/o'neil story with the murderer dressed up like santa clause...