Littlel dog lost is all I can remember

Is it a kids' book? Is that the title? (There are several titles like that.)

http://www.amazon.com/Little-Dog-Los...524351-9213123 -- On a cold winter day, a curious dog wanders onto a frozen river. Suddenly, the ice starts breaking up, and soon the dog is adrift and traveling–the unwilling passenger on a fast-moving sheet of ice.

http://www.amazon.com/Little-Dog-Los.../dp/0688511392 -- This classic children's book tells the story of a Welsh Corgi puppy who gets lost in the woods and is adopted by a mother fox. He learns to survive in the wild as a fox, but is found at Christmas by humans and adopted by a little girl. The Corgi later goes back to the woods to help his injured fox mother, who eventually comes to live at the farm woodshed under the care of the Corgi's human family.