Even with the benefit of a green house over wintering plants can still have its problems, a common one being Grey Mould. This is a disease which thrives in damp conditions combined with poor air circulation, a common combination in wet dank winter months. Tips to avoid grey mould are not to pack the plants in too tightly into the green house or cold frame and ventilate as much as possible. On mild days open up the doors and vents to improve air flow. A good idea is to raise the plant off  the ground which has two advantages. Its avoids the plant being on the very cold ground during periods of severe weather but also keeps the air flow underneath the plant as well. To raise the plant it's really easy to make some low trestle  or supports using couple of old bricks and a plant as shown in the photo here.

As much air flow as possible to prevent the grey mould and if you do spot it remove leaves, clean up around the plant and if  it had taken a hold with the plant remove it so prevent infection to the other plants.