Actually there are micro-organisms that can survive in space. They are part of a group called extremophiles.
Extremophiles have been found in incredible places volcanic vents for example, in nuclear reactors and attached to spacecraft.
You also have to be carefull about assuming that space is cold. In deep space that is certainly true but in Earth orbit, in sunlight things can hot up a bit.
Interesting little calculation here for the temperature of a simple flat plate in orbit - comes out at 394 �K which is about 120�C.
http://www.grc.nasa.gov/WWW/K-12/Numbers/Math/ Mathematical_Thinking/estimating_the_temperatu re.htm
I'm not expert inough in micro-biology to know whethere extremophiles would be able to decompose a body but it's certainly not as simple a question as it at first sounds.