The front door of my house (which is rarely ever used) sweats so badly during the winter. At first I thought it was just the glass, but after a closer look it appears that the rescued areas are also sweating. I have not yet installed a storm door, could this be the issue?
Condensation occurs when moist air contacts a cooler surface. Adding a storm door will make the inside surface of your front door less cool, and may help reduce the condensation. You may also have excessive humidity from (for example) showering without using an exhaust fan, cooking, etc.
I would suggest getting a device that measures relative humdity (Here's one example of many that appeared when I searched "indoor humidity" on Amazon; to see if excess humidity may be part of the problem (note that recommended levels vary with the outdoor temperature).