You’re right, it is water. One of the products of Burning of hydro carbons is water - when the exhaust is cold it condenses and collects / drips from the exhaust. When the system has been running for a while it’ll get hot enough that the gases don’t hit their due point and any existing condensed water should evaporate and be carried away with the flow of exhaust gasess. On really cold days you can usually always see the exhaust gases when the car is stationary.
It obviously catches some of the particulates / exhaust fumes and is a little nasty and that’s why maybe you thought it was something else.