The white smoke is coming from relatively incomplete combustion, or from steam. Could be dripping fat, wood, bad or moist charcoal/lump, lots of things.
I have seen it in the situation you describe; temps falling low and the subsequent stoking of the fire to get temps back up. It usually only lasts an hour or so until you get things stabilized, if that is the cause.
Bottom line, don't sweat it. I've cooked with the thin blue stuff, as well as heavy-duty-pure-hickory-burn-your-eyes-out-cough-up-one-lung smoke, and have fine results on long cooks.
-elbows deep in someone else's misery.