The glass is simply the coldest surface in the room. Warm air holds more water than cold air, and when that air touches something cold enough, it gives the water up. Your window is the first place in the house cold enough to show it — which makes it the only visible warning you get.
The air doing that to your glass is doing it everywhere else it meets a cold surface. You just cannot see those.
It is the same thing that happens in summer, pointed the other way
In July the hot wet air is outside and the cold surface is inside — the supply vents, the ductwork, the wall behind a register, the side of the house the air conditioner is working hardest on. Moisture moves toward the cold and gives up its water there, usually somewhere you cannot see it.
In January it flips. Now the warm wet air is inside and the cold surface is the glass. Same physics, opposite direction, and this time it happens somewhere you can watch it.
That is why it is worth paying attention to. Six months of the year the condensation is hidden inside the building. For a few weeks in winter, the house shows you.
What it is actually telling you
The air in that room is carrying more moisture than the room can hold at its coldest point.
Mold needs sustained moisture, and it does not need a leak. Above about 60% relative humidity, growth becomes possible on ordinary building materials with no water intrusion at all. Condensation on glass means you are at or past that point somewhere in the room, for part of the day at least.
That is the whole warning. Not "your windows are old." Your air is wet.
Where the mold shows up instead
The glass dries out in the morning. These do not.
Exterior walls behind furniture. A wardrobe or a headboard against an outside wall stops air moving over that surface, and that surface is already the second-coldest thing in the room.
Inside closets on outside walls. Closed door, no airflow, colder than the room, full of fabric.
Window sills and the trim under them. The water that ran off the glass goes somewhere. Usually into the paint line, then into the wood.
Behind curtains and blinds. They insulate the glass from the room's warm air, which makes the glass colder still.
Ceiling corners on exterior walls, where two cold surfaces meet.
If you have condensation on the glass, those are the five places to look, in that order.
Why it shows up here, where it barely gets cold
You do not need a hard winter for this. You need a cold surface and wet air, and in this climate the air is the easy part.
What changes in December is the other half. The air conditioner has been pulling moisture out of the house all year, and then it stops running. Nothing about the house changed. The thing that was drying it went quiet.
Some windows do this far more than others
The temperature of the glass is what decides it, and that depends on the window. A single pane sits at very close to the outdoor temperature, so it starts giving up water at indoor humidity levels a modern window would shrug off. A double-pane unit, especially a low-e one, holds the inner surface much closer to room temperature and stays dry through conditions that would run a single pane wet.
So two houses on the same street with the same air can behave completely differently. If yours are single pane, a little water on a genuinely cold morning tells you less than it would in a newer house.
But it cuts the other way too. If the glass is that cold, the surfaces you cannot see — exterior walls, closet corners, the wall behind the headboard — are colder than they would be in a better-built house as well.
When condensation is normal and when it is not
Normal. A cold snap, first thing in the morning, a little water at the bottom of the glass that is gone within an hour or two. A bathroom mirror after a shower.
Not normal. Water that is still there in the afternoon. Water running down and pooling on the sill. Condensation on more than one side of the house. Water on glass in rooms nobody is showering or cooking in. Any of it happening alongside a musty smell.
Different problem entirely. Fog between the panes of a double-glazed window is a failed seal in the glass unit. That is a window issue and it has nothing to do with the air in the room.
What to do about it
Wipe the glass and the sill, so the water is not sitting on wood — but understand that you are treating a symptom.
Then deal with the air, which is a different subject and has its own page:
How to lower the humidity in your house
And if you are seeing condensation and smelling something musty, the condensation is no longer the early warning. Something has already been wet long enough.