If the operating door is not removed prior to painting, it will be difficult for the painter not to get paint on the weather-seal and this will adversely affect the ability of your door to keep out the cold. And, after the paint hardens onto the weather-seal, you will likely notice a scrapping sound as the door is moved open and closed. First removing the door will actually save the painter a little time as well.
Have a handyman or contractor remove the door for the painter, place atop some sawhorses and then return to replace the door when the paint dries. This will cost you a few extra bucks, but the job will be done right and have a professional appearance.
Without the door being removed, it will be impossible for the painter to reach the seven-foot by three-inch vertical area (from top to bottom) on the operating door and the stationary panel where they interlock.
If this was never done years ago, take the opportunity to paint these sections and replace the damaged weather-seal the next time the door is removed for service.