Sounds like you should take it to an exhaust shop - might be a broken mount, broken baffle, anything.

Condensation doesn't increase due to it being more cold. Some of the by-products of exhaust fumes are hydrogen and oxygen which bond in gaseous form. When your car cools, these move from gas to liquid state and ends up sitting in your exhaust, cat etc (which is why exhausts are prone to rusting out over decades). When you re-start the car the next morning, the exhaust heats up quickly and has more H20 being pumped out as steam due to the build-up. Then it reverts to normal once all of the residual water has been expelled from the system.

Ignore "fumes smell"... all fossil fuels smell. In fact, you shouldn't be deliberately smelling an exhaust given all of the carcinogens etc that are being pumped out of an exhaust. If you wanted to see how much water comes out of a tailpipe, start up your car from cold and put your hand over the tailpipe- you'll end up with a sooty, wet hand. Don't leave it there too long though and don't breath in the exhaust fumes.