Enclosed porch areas are prone to frost accumulation. A door opening from inside to a cold porch allows indoor humidity to escape into a closed space where it condenses on cold surfaces. If the weatherstripping on the wood door next to the storm door is worn or absent, moist air can leak into the space between the interior door and storm door. Your old storm door may have had a looser fit than the new door. Your tight-fitting new door traps the moist air in the area between the storm and wood door, causing frost to accumulate on the metal storm door.
Most storm doors have adjustable sweeps at the bottom of the door.
Adjust the door bottom up, providing an opening at the bottom of the door where the moist air can escape to the outside. To keep warm moist air from leaking into the space between the wood and storm doors, check the weatherstripping on the wood door and upgrade if necessary.