Hi this appears to be a mould, called i think Botrytis.You will need to remove the leaves carefully as it can spread, ensure you have good ventilation in the greenhouse and that the plants are not too damp and close together,
hope this helps a bit.
daz

The biggest enemy of pelargoniums is damp, cold conditions - they will withstand up to 10 degrees of frost, but what kills them is mould/rot of the type you describe, caused by damp/wet, which is more likely to occur where movement of air is limited, and where the plants are crowded together. Best way to overwinter is to reduce the topgrowth by two thirds, down to about 6 inches, remove any leaves left behind, dust with sulphur dust, all done in autumn. No watering, and regular inspection essential to remove any leaf drop (these will encourage growth of moulds) from the top of the soil/compost, removal of any plant with signs of mould, and with the door or window being opened whenever possible to encourage good airflow if your greenhouse is unheated.

Snap mine have done the same. Too cold and too wet. But when the snow came I couldnt get to the greenhouse so that is that.