White smoke equals dirty smoke. The smoke you see should be very light, whitish blue in color. The less smoke you see, the better.
Thick white smoke is an indicator that you are not getting a clean burn, and you need more oxygen intake into the kettle.
This means you will have to burn a hotter fire.
The worst smoke is that thick, white smoke, with a tint of yellow or gray. You do not want that on your food.
All of my snake method smokes have resulted in very little smoke, and the smoke that appears is blue, not white.
I only use B&B charcoal, and good quality hardwood (Oak / Hickory) for smoking on the kettle.