How can I repair a bathroom fan under garage that is leaking in the winter?
The vent should be going directly outside, not venting inside the attic near a screen.  Also, the pipe should be covered in insulation to prevent the warm humid air from cooling down so much that the water vapour condenses and runs down the pipe into your bathroom.  This might be damaging your ceiling drywall, which is a pain to repair.


Extend the pipe through the exterior wall.  Use an exterior vent with a damper, so wind does not blow cold air into your house in winter.  There a a couple of different types of dampers, and the vents come in many colours and sizes to suit the exhaust pipe (can be various shapes and sizes), a 4" round vent is most common in North America for bathroom venting.  This can wait until February (it's already been years, I'm guessing - so another month shouldn't make any significant difference).
Insulate the pipe.  You can get pipe insulation that slides over the pipe.  If possible, you should do this now, to stop any further water damage.
If your insulation is soaking wet, replace it.
Repair your drywall if there has been water damage.  Be sure to use a stain-blocking primer before repainting the ceiling.