A person's normal body temperature is 98.6 degrees Fahrenheit. It takes a long time for the body's core temperature to drop based upon its ability to protect itself. That being said, one needs to look at this in a couple different ways.
1. If a person is to go out into 20 degree (Fahrenheit) temperature, and the person is dressed appropriately, it will take a lot longer to freeze to death. As stated before, the body has natural mechanisms built in to try to insure the body keeps its core temperature. The body shivers and blood flow moves to the core in order to protect the organs.
2. If a person is not dressed properly (no coat or warm clothes), it will not take as long to freeze to death.
Regardless, a person's body temperature must drop to 78 degrees in order to insure their death. Prior to that, at 82 degrees a person can lose consciousness and at 91 degrees a person can experience amnesia.
Another thing a person must keep in mind is the the water in one's body contains salt. Water with salt in it freezes at a lower temperature than water without. While 20 degrees is certainly lower than what water needs to freeze at, the body provides a protector to the internal organs and fluids in the body.