About 24hr or so to dry brine it and let the skin dry out in the fridge (optional step, you could just season it and put it right in the smoker). I used my grill, so I also had to start up a fire and get it up to temp as well, which took around an hour. After that it's just monitoring the temp occasionally, and I took it out about twice to remove the goose fat in the pan.
Looks delicious. I like goose, but we have several people in the family that won't even touch the dark meat from a chicken, so goose is off the table. :(