Question: If a plane without any deicing equipment has water moisture on the wings (say, from sitting overnight) and that plane is then flown to an altitude which will have temperatures below freezing, what is the risk of that initial moisture causing icing concerns? 

For the sake of hard examples:

* Plane: Piper Cherokee 140
* Air temperature on ground: 40°F (4°C)
* Air temperature at cruise altitude (3500ft): 28°F (-2°C)
* No visible moisture in the air, the only moisture is the moisture on the wings prior to takeoff.

Questions:

1. Will this be a problem?
2. If it is a problem, what is the best course of action to protect against the icing concern?

Answer: 
Taking off with wet wings is not a problem, the airflow is going to blow the water off long before it reaches the freezing point. There's no concerns here. 

Given the scenario what I would be concerned about would be ice elsewhere on the airframe. 40°F (4°C) could mean that the aircraft was frozen overnight, and there could be ice left over where the sun didn't melt it off. That kind of ice wouldn't necessarily impact the airflow on the wing, but it would make the airplane heavier and therefore impact performance. A simple visual check on the walk-around will confirm this. If there is ice left then deal with it even if it's not on the wing or tail, if it's just wet then get in and fly.
With 20,000+ hours in everything from L19 Bird Dogs to Gulfstreams I though I should offer these thoughts/facts. The most remarkable and pertinent being my own experience with moisture freezing on takeoff. Ambient temperature was +2 C according to ATIS. Light rain had soaked the top of the wings on the King Air 200 I was flying. Immediately after flap retraction the airplane began to roll to the right. This was corrected with left aileron and we decided to return to land. On final the copilot looked out at the right wing and observed patches of frozen water droplets on the top of the right wing. As we landed back into the +2 C air, much of the frozen droplets blew off, however some still remained on the aft, inboard sections of both wings. I consequently contacted a source at NASA’s Icing Research unit at Cleveland Hopkins and he confirmed that the low pressure created on top of the wings as it accelerates on takeoff May cool the wing and water droplets to the point of freezing during takeoff BEFORE they are blown off. On critical wing surfaces we find on today’s aircraft this could have a negative effect on lift and cause control issues due to loss of lift. Since this experience 25 years ago or so I have ALWAYS addressed any moisture present on lifting surfaces when he ambient temperature sits within a couple degrees of freezing either with anti-ice treatment or manually removing the moisture. Once you’re airborne with a rolling airplane it might just be too late.