For six weeks something that runs when it's cold outside has caused shaking of the floors. There is a transformer for the powerlines at the back of the property. Neighbors to right and left don't notice anything. What can be the cause? Thanks.
Transformers do vibrate a little due to magnetostriction. You often hear buzzing or a hum when close to a high voltage transformer, this is the transformer vibrating at the mains frequency.
The greater the current passing through the transformer, the greater the amplitude of vibration. In your case, cold weather may result in more power being drawn by the connected buildings.
For this vibration to affect your building, there must be some conduit by which the vibration can be transmitted. Transmitted with enough energy to get your floors resonating. It seems a long shot but it may be possible. When you feel your floors vibrating, check closer to the transformer, can you feel the ground vibrating?
Densely packed European city center buildings (including residental buildings) sometimes have their power transformers right in their basements.
Very, very quiet 50Hz hum is sometimes audible at night on the first floor and that's it.
(I am not saying that this practice has no flaws. But the vibration is not one of them).