What is the difference between a cold-stream thrust reverser and a conventional one? It seems that all engines emit hot air, due to the combustion process.
Turbofan engines don't push all air through the combustion chamber. Instead part of it runs along the sides.
This bypass region is where the (cold) air stream is redirected from to create the reverse thrust.
Not all air that flows through a turbofan engine undergoes combustion. In a turbofan, part of the air (in some engines, most of the air) is bypassed around the power turbine; that air is simply accelerated by the compressor fan and is vented, cold, out the back of the engine to provide thrust.
A cold-stream thrust reverser simply deflects this cold, bypassed air forward, whereas a "normal" thrust reverser deflects the main engine exhaust.
Wikipedia has some pictures and more description.