It does, but most of it evaporates.
I tried it when I was a little kid, using two ice trays and my parents freezer. Boiling water/hot water will make ice cubes before cold water. But, they are only about 1/4 the size of the regular cubes.
"Hot water can in fact freeze faster than cold water for a wide range of experimental conditions. This phenomenon is extremely counterintuitive, and surprising even to most scientists, but it is in fact real. It has been seen and studied in
numerous experiments. While this phenomenon has been known "For centuries, and was described by Aristotle, Bacon, and Descartes
[1–3], it was not introduced to the modern scientific community until 1969, by a Tanzanian high school pupil named Mpemba. Both the early scientific history of this effect, and the story of Mpemba's rediscovery of it, are interesting in their own right — Mpemba's story in particular providing a dramatic parable against making snap judgements about what is impossible"
http://math.ucr.edu/home/baez/physics/General/hot_water.html