White smoke is just water...Given your less than dry location, it's absolutely normal to have some moisture in the exhaust upon start-up.
Most dual exhaust systems have a thermostat that keeps one pipe closed until the engine warms a bit, so you'll almost always get the white smoke out one pipe until the thermostat opens.
After driving the car for 10 minutes or so does it go away?
If it doesn't go away, check to make sure you're running cool, because that can be a sign of a head gasket beginning to fail.
Also make sure what you're seeing isn't "the blues," which means blue oil smoke. The easiest way to tell is to put your hand behind the car when it's coming out. White smoke makes your hand wet. Blue smoke smells like oil and has little moisture.
If it is indeed blue, then you have tired engine internals (like rings.)
My guess is that it's just normal moisture.