I have hot smoked on a bbq (essentially baking in smoke) but don't know how you would cold smoke in it as it gets too hot inside. You would need a way to channel (dryer conduit works great) the smoke from the bbq to a container holding the fish (ie: small bar fridge) which allows the smoke to cool before it gets to the smoking chamber (cold smoke).
That said, hot smoking pinks on the bbq is still very tasty. I pack my fillets in brown sugar for a few hours to draw out the moisture. I then fill a foil packet with wet wood chips (soak them at least an hour so they do not burn too fast). I make the foil packet large enough to cover the entire grill so the flames never make contact with the fish itself. I heat the chips until they begin smoking, then I open the bbq to cool the chamber Down and lower the heat to minimum needed to keep chips burning. I then place the fish on wire cooling racks over a foul lined cookie sheet. Then let it smoke for about 1/2 to 1 hour. The bbq will easily get over the 80 degrees F that is the definition of cold smoking (usually around 300-400 degrees depending on the heat needed to keep the Chips burning), so it is essentially baking the salmon in the smoke.