Welcome to the 405th! You can probably start building your costume now and by the time you're ready to paint, it may have warmed up a bit. Make sure though that you've still got plenty of ventilation wherever you're building your armour for things like glues, dust, and other things lungs don't like eating.
It can be pretty hard to do spray paints in colder weather. If it's freezing out, waiting until it warms up is a good idea, unless you have a warm, well ventilated space you can do it in. One thing you can do is put spray cans in a bucket of warm water for about 10 minutes to help break up any clumps inside.