I have done quite a few geese. You didn't say domestic or wild. There is considerable difference. Domestic are bred for their big breast and since they don't fly, have little breast muscles. The breast is quite tender and white meat. Wild are narrower to cut the wind, have more muscles and are ususlly quite a bit darker meat and quite lean. Brining is good with any bird but especially helpful on the wild ones.
Regardless of which you are smoking, when smoking, I treat them just about the same as Turkey. Brine, inject and smoke/cook at 275F-325F. Looking for an internal temp of approx 165F minimum. I prefer 170F.