Quebec city has a tough winter but, while I have never spent a winter in Ohio, I suppose you might experience something similar.
The temperature in Quebec city in February is probably more in the -10/-20F (-20/-30C), the 5F (-15C) are usually reached as soon as December and Wikipedia lists 5F (-15C) as the average morning temperature.
It is probably worth being careful about dressing appropriately with one of the heaviest gear. The carnival happens outside so not only will the temperature be cold but you will spend long periods of time outside, maybe without moving much (while when it is that cold, on a daily basis, I suppose you do not stay more than an hour outside without entering a building, or you do physical activity which warms your body up).
That said, you seem to be used to a cold area as well, so you probably have experience with low temperatures. Just be prepared with your gear for the cold, and do not hesitate to go inside and/or get some hot beverage. Also, gear for this low temperatures need not be super expensive, but still in the hundreds of dollars (and I have indeed heard Quebeckers investing around 500 -1000 dollars in their winter coat).