First off, the engine light on the car has cut on and there are a few codes indicating a small leak in the evaporative emotions system.
Secondly, with the recent tempeture drop in my area, my 2003 honda accord V6 has been underpowered, also it runs rough a few seconds at a time when maintaining speed. I have noticed these seconds of roughness usually happen around 1500 RPM at 35 MPH and around 2000ish RPM in the 55-70 MPH range.
Could these issues be related and if so what is the most likely culprit?
When was the last time the engine was serviced?
How many miles are on the car?
Low power and rough operation are more often the result of overdue engine servicing than not.
But in this case, you have fault codes stored in the ECU, and if you’ll answer the questions and post the actual codes we might be able to get to the root of the problem a lot quicker.
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+1 to mountainbike’s advice, but I have an additional thought.
If the problem lies in the car’s Evaporative Emotions System, perhaps the car just needs a tranquilizer. 
I’m sorry.
The Devil made me write that…
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For the record, I’d like to add that there IS an EVAP system problem that can cause your symptoms. And the root cause could be the habit of “topping off” the gas tank.
The actual codes would be a great help.
The first step is to get the code evaluated and the cause found. There are Evap problems that can cause the poor performance you describe. However, evap codes don’t always point to a quick and easy solution, and an experienced auto tech needs to narrow down the problem.
Suggest to post the diagnostic code numbers that were stored in the engine management computer. That will give folks here more of a clue what may be happening.
There’s a couple of experiments you could try if you wanted. When this happens, see if it happens the same way when selected a fixed gear (like “4”) vs driving in D, presuming you have an automatic transmission. And see if you still notice any roughness to the sound of the engine when you shift to neutral and let the engine idle while you coast.
As mentioned above, the way shops handle this problem if they can’t see anything obviously wrong is to read the codes first, fix whatever is causing them, and if the problem remains they’ll bring all the routine maintenance up to date. And they’ll check out the entire vacuum system. If the problem remains, they’ll start with the fuel pressure, ignition system, and compression tests.