The short answer is, it depends.  Depends on what?  Well, if you are like me and swimming is not your strength (or if you are absolutely terrified of the concept of venturing out into open water), it depends on whether the race allows you to or not.  If they are permitted, again if you are like me, then sprint to the car and grab your wetsuit and don’t take it off until you have safely completed the swim portion of the race and a kind volunteer will strip it from your soaking body.

The longer answer also begins with it depends as there are several variables (other than terror) that need to be factored into the wetsuit decision.

Are you allowed to wear a wetsuit?

There is a difference between the use being not allowed and not sanctioned.  The temperature of the water is the variable that distinguishes these two notions. 

Water that is below 50 degrees F is not suitable for open water swimming – even with a wetsuit. 

Water between 50 and 65 degrees is suitable for open water swimming. A wetsuit is recommended but not required. 

Water between 65 and 78 degrees is suitable for swimming with or without a wetsuit. 

Between 78 and 84 degrees, the Race Directors will make a race morning decision whether or not to permit the use of a wetsuit.  In this case the directors have two options. They can either sanction the use of the wetsuit or simply allow it. If sanctioned, then placings, qualifications, and prizes will not be affected by your choice to wear a wetsuit. If simply allowed, then you may elect to wear one but you will not be eligible for a spot on the podium, prizes or qualification to championship races. 

If the water is higher than 84 degrees, wetsuits are not permitted.

Are you a strong swimmer?

Your ability as a swimmer may also come into play in your decision (assuming the water temperature permits their use).  Weaker swimmers tend to crave the added buoyancy (and confidence) a wetsuit provides, whereas strong swimmers often prefer to swim as close to naked as possible.

What are the water conditions?

The conditions of the water may also be a factor.  If it is choppy or there is a large swell, the buoyancy of the wetsuit will act as a safety blanket allowing the swimmer to worry less about fighting the water.

How much training have you done?

The amount of training you have done will also be a factor.  If you have been training regularly without the use of a wetsuit and you are strong, then perhaps there is no real need to wear one.  If, however, you have not been in the pool much in the weeks leading up to a race, perhaps donning the wetsuit will offer a slight advantage as it will keep you afloat.