This is what I have at home. We have the same type of addition with 2 gable vents working 'together' with soffit vents. The addition is 30' x 15'. It's on the North side of the house and gets virtually no sun on the roof for 6 months. I used Snow 'N Ice Shield before I put the shingles on. Plus, I used a 30 year shingle. Fortunately, I don't have to shovel my roof even though it's a 2-10.
In short, the passive venting should be fine!
Jay J -Moderator
PS: If you add a fan, you'll end up drawing in moisture from the outside where it may/will condense beneath the roof (depending on the climate and where you live.)