TL:DR - No, you don't need to change the oil.
The reason some manufacturers like Honda and Subaru have moved to 0w oils is for fuel efficiency, because 0w oils flow better when cold than 5w oils the resistance in a cold engine is lower, meaning a small gain in efficiency and a bit less wear at low temperatures.
The actual difference is marginal in your case, the operating temperature of 0w oils is down to -40°C (-40°F, not a typo, this is where the scales meet), whereas 5w oils it's -35°C (-31°F). As you are getting nowhere close to those temperatures there will be little difference in the viscosity of your oil when cold, and it could cost far more for you to replace the oil than you'd ever save in mileage.
If you lived in a much colder climate it would be more of a consideration, but I still wouldn't replace the oil just for that reason, it would have to be too close to the lower operating temperature of the oil.