Cold is a good thing for non-DPSS lasers. One major downside is condensation which
will fog up exposed optics and leave moisture on everything not sealed. Lasers
like 445nm will give more output (safely) and in red lasers can drop the wavelength
a little making the beam slightly more visible. Though the difference is temporary
and possibly not even noticeable.
If the laser is small enough to fit in your pocket close to the body, you can
keep it at perfect temp.
If your laser is green / DPSS, the cold will just drop down the output until it
warms back up, and condensation remains an issue..