How can I stop my windows from leaking when mild winter weather occurs?
Are you saying that you manually insulate the window on the inside with foam board to prevent heat loss? If so, this is completely expected. What's happening is that the insulation is doing its job by preventing the movement of heat, thereby keeping the glass colder. However, it sounds like the installation is not airtight. As a result, any moist air that goes through or around the foam board and touches the glass finds the perfect surface to condense on: something vertical, hard, and cold. So it does. If you want to manually insulate a window on the inside like this, the insulation must be absolutely airtight to prevent condensation. The more expensive but more correct solution to the problem would be to replace the window with a higher-performance one, likely a triple-pane. Low-E exterior storm windows are good too, and a lot cheaper, but that might be hard to do on a bay window.