I'm not sure if this is the textbook explanation, but this makes sense to me:
[D = capital delta]
Consider the process of dissolved gas escaping
A(aq) ---> A(g)
now, think about DG for this process:
DG = DH - TDS
The more negative the value of DG, the more favourable the process. Think about the sign of DS (entropy change). Is it + or -? In which case, what effect will lowering the temperature (T) have on DG (assuming DH is temperature independant)?