Well, first off can you please give us some more information. All we know right now is that you own a laser. Whether its a 1mW red or a 1kW CO2, or, as I'm guessing, a greenie can make all the difference.
So, lets assume its a green. In that case: no. First off, the crystal set that is used to take 808nm to 532nm is very sensitive to the input wavelength. As the input wavelength changes even slightly, efficiency goes down significantly. Unfortunately, what chances input wavelength? Temperature. At 0C, there's a good chance your absorbtion and efficiency will be ~0%, meaning no output. Even if you can get output though, the KTP crystal will probably not be too happy being pumped by so much energy at so cold a temperature. Not too sure on the details here, but you may overstress and damage the crystal by doing that (again, meaning no output, but this time its permanent).
So basically, if you have a green laser, the answer is no. If its a red, more than likely it will only get better with cold, but you'll have to let us know more details.
The laser would never be cooled to outside temperature anyway unless you left it outside in the shade for an hour. The very operation of the laser generates heat which would keep it from dipping below the recommended minimum operating temperature.
Store it indoors, keep it in your pocket when outdoors and not being used and you'll be fine.
In that case, please refer to my post earlier. You're not likely to get favorable results with that laser at 0-5C. Even if it does lase, you'd be putting undue stress on it. The diode would love the cold weather, but I'm not so sure about your crystal set.