Your best solution may be to just tarp off the problem area until the spring but be sure not to block off any venting pipes that vent out dangerous gasses.
Fix leaky roof in winter.
The shingles can be warmed up with a propane torch.
Shine a flashlight along the underside of the roof and look for a hole in the roof as well as areas that are wet or have been.
How to repair a leaky roof from inside the house.
While most homeowners aim to repair their leaky roofs during the summer winter roof repair is always available when you need it.
For example soak the downhill side of a chimney first then each side then the top on both sides.
The purpose is to keep the shingle tabs down in high winds.
Identify the potential source of the leak.
If a leak is difficult to find enlist a helper and go up on the roof with a garden hose.
You can t fix a leaky roof from the inside so don t even try.
Replace any missing or rotted siding above the step flashing on dormers.
Isolate areas when you run the hose.
The roof shingles should be softened and flattened as the shingles tend to curl up in winter.
Make use of the flame carefully on the curled shingle edges.
Recaulk the corner flashing if any areas have hardened caulk.
Locate the source of the leak by examining the underside of the roof from within your attic or crawl space.
Now is a time when you can start planning if you know where to start.
If you plan to replace shingles in the winter it can be done but you have to add something to bond the shingles together.
Start low soaking the area just above where the leak appears in the house.