Doors and Windows - condensation outside at front door

We have a steel front door -- what appears to be solid wood with a layer of steel on the outside and another on the inside. The door leads into an "air lock," if you will, with a second insulated door leading to the living room. We are having continual problems in the winter with condensation that often freezes around the brass door lock on the outside only and along the rim of the outside layer of steel, principally in the area of the lock but sometimes a bit above it. On rare occasion, the door is actually frozen shut. We are replacing the lock, which no longer works, but would like to eliminate the problem so that we don't have to face more problems.

Note: there is no condensation inside, either on the inside layer of steel or on the parts of the door lock that are on the inside.

You don't say where you are, but it must be COLD. It sounds like the inside door is leaking warm/moist air to the mudroom space, which then freezes on the outside door. Check the inside door and spaces around the door for air leakage from the house.

The "air lock" contains two large plants, so there is inevitably moisture inside, but with the ice on the outside only and the door quite tight fitting, I wonder that that could be the source of the moisture, which accumulates around the outside lock and a little on the outside edge of the steel envelope.
We live in the mountains of West Virginia, and yes, we've been having some cold weather (as low as 3 degrees of a morning). The door is sheltered by a concrete overhang and I suppose that some of the drip from it might splash near enough to the door to cause a problem, though I question it. We have a deck wrapped partly around the house, with one end outside the air lock. The deck ends there with a storage closet, and moisture is a problem there as well.

My guess would be there is water under the deck in that area. It is evaporating up through the decking boards into the storage closet and also in front of the door. The brass lock, being heavy made metal, gets colder than the air causing the frost to be on the lock. The door is not as heavy a metal, but if the lock gets frozen enough, the metal on the door surrounding it will also frost up.
See if water is pooling under the deck in that area. Is the ground saturated with moisture? Add dirt to the low area to keep the ground dry as possible to stop the moisture draw.