I smoked a whole chicken with the skin on it and it did not have a smoky taste.
My question is whether removing the skin will improve the depth of the smoke flavour the next time I smoke a whole chicken.
I wouldn't recommend smoking any whole poultry without the skin as it may dry out the meat. You would have to be constantly basting it and that would throw off your cooking time and temperatures due to keeping the lid open to often.
Not knowing your cooking technique, I can only guess at a few things. Either you're not cooking it slow enough to allow the smoke to set in or you're not using enough smoke. I like to cook very low at about 185 to 250 for a few hours with plenty of visible smoke then I raise the temperature to about 350 to 375 to finish it off keeping the bird close to the heat source so that it crisps the skin slightly.
Some other advice would be to avoid checking the bird often. It's tempting to see what's going on under that lid but if you lift the lid to often you're letting all that good smoke out and losing the flavor.