I think you are on the right track. If the ice door isn't sealing all of the way, then you will see frost build up around the dispenser area inside the freezer. The ice door has been re-designed and it is now made from a different better material that doesn't require the heater on the ice door. If yours is an older model that has a heater, and the heater has stopped working, then it could be causing your problem. Typically, there is more humidity and moisture in the air during the warmer months of the year, so that would also make sense.
Are you seeing any frost build up in the dispenser area inside the freezer?
Ice Door Kit - 8201649