I used 2x8 rafters to span a 24' barn with a 60 lb design snow load. The roof had a ridge beam making the span 12' each way.
Checking my span book, your 2x8 rafters will allow a maximum span of 17 ft. 5 in on 24" centers with a snow load of 20 psi. If you are in a heavy snow area (50 lb), the span drops to 12'4" and is still OK. I am going to agree with Jason that your rafter selection is conservative and should be fine. Recommend you add collar beams or brace your walls to prevent spreading.