That highly depends on the temperature. Any temperature below freezing point 0˚c (32˚f) can be dangerous if your child is not dressed properly.
Generally if the child is dressed properly for the weather, a half an hour to one hour of outside play in the above mentioned temperatures, wont hurt him/her. In snowy days, parents like to let their children go outside to play. Unless the child is at least 10-12 they shouldn't go alone outside at all.
Young children should be accompanied by an adult, specially if there's water nearby. In days in which the temperature seems to go down suddenly, lakes and rivers can slowly reach lethal temperature levels. Even when the water doesn't freeze, the temperature is still too low for any human to survive.
If a child should fall into a river or lake, he/she should be immediately brought back inside. Clothes should be changed for dry clothes and a glass of warm fluid, like soup or chocolate should be given to avoid shock (and death) due to hypothermia.
Any temperature below -6˚c (20˚f) can be dangerous even if your child has the right clothing. I recommend do not let your child outside in any temperature below -6˚c (20˚f) for more than 10-20 minutes.
Most important of ALL, pay attention to what your child tells you. If he/she tells you he/she is cold, regardless of temperature; its time to head back inside. :)
See also (a nifty temperature converter you might like to try)!: http://www.wbuf.noaa.gov/tempfc.htm