No Problem! 
The biggest problem I've had with cold temps & laser projectors is that the individual laser modules are effected differently, so while the overall laser power "could" be reduced, it could also really mess with your color balance. Only way to know for sure is to cold-soak the projector and see what happens.
Whether or not the 3 watts is "enough" depends largely on the surrounding ambient light, but more than likely that will be plenty.
You'll definitely need to make sure that your projector is setup so there is no way for your visitors to walk in front of the beams.
(Which could be quite challenging for a home outdoor display!)
You'll probably want to run some display tests with your projector and find out if the graphics image size you want will work with your planned outdoor placement.
Safety concerns may dictate that your projector is placed relatively close to your display screen area, which could require that you run a fairly large scan angle on the projector.
Graphics images at large scan angles tend to really work the scanners very hard, and can result in poor image quality, and in some cases, damage to the scanners.
(As I found out the hard way with my original projector build...
).
One more item to think about -
Anything you do with your laser projector outside is going to open you up to public scrutiny, liability concerns, etc.
Given the bad rep that lasers in general have received lately due to morons with high-power laser pointers, you may want to weigh the pros and cons.
All this said -
Everything you've posted indicates to me you intend to take a very safe approach and should be fine!
Last edited by Stuka; 10-26-2015 at 04:33.
RR
Metrologic HeNe 3.3mw Modulated laser, 2 Radio Shack motors, and a broken mirror.
1979.
Sweet.....