Why can the inside of a window fog up on a cold day?

Answer: Water vapor in the room turns into droplets on the cold glass

Water vapor in the room turns into droplets on the cold glass ✓ — Water vapor from indoor air condenses when the glass is cold enough. Below the air’s dew point, droplets can collect on the surface; higher indoor humidity makes this more likely.

Cooling makes the glass release water stored inside it — The droplets are not water released from a store inside the glass. They come from the air, which is why a cold drinking glass can also become wet on the outside.

Outdoor moisture seeps through the solid glass into the room — Surface fog does not require outdoor moisture to pass through solid glass. Indoor air supplies the water vapor, so even a closed, unbroken window can become wet on its room-facing side.