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.
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As GdD mentions, this wont be a problem as most of the moisture will blow off by the time you get to the runway. I have had this occur on occasion on the Warriors and Archers I trained in, it was never an issue. 

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Straight moisture is never an issue but you should always confirm that this moisture is not the result of ice underneath. Here in the northeast there were some mornings where moisture on the wings froze over night if temperatures dropped enough. During sunrise this typically melted off but for an early morning departure this needs to be tended to. The best course of action is to either wait it out, usually by the time the sun is up over the horizon the ice will be melted off, or have the aircraft de-iced. Even small airports usually keep some de-ice fluid on hand.