That is pretty much what I have, except mine goes out through a window. The room is odd, I think when the house was built, it was all one room, and somewhere along the lines before we bought the house, someone in their infinite wisdom decided to put a wall up to create 2 rooms, and to separate off the water heater, water tank, etc, etc. Only problem is, the wall they put up they had it right in the middle of an existing window.
So basically what I did was took a piece of plywood the size of the window opening, dryer vent on the outside, hose on the inside going to the booth. Then put in a piece of 2" insulating Styrofoam, and then one of those window seals...you know the kind you put up with 2 sided tape, and shrink it to fit with a hair dryer to seal it off.
Still get cold air coming in through the hose when the booth isn't running. Again, piece of 2" insulating Styrofoam to the rescue keeps most of the cold at bay from coming back in the house when not in use.