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 a leaking roof in winter.
Recaulk the corner flashing if any areas have hardened caulk.
Sealing the shingle to the object can be accomlished with a roofing sealant available at menards lowes etc.
Locate the leaking source and search for the damaged or missing shingles and make a list of the areas to be repaired.
Now is a time when you can start planning if you know where to start.
Shingles that aren t stuck to one another are very susceptible to damage in winter winds.
Make use of the flame carefully on the curled shingle edges.
Replace any missing or rotted siding above the step flashing on dormers.
If a leak is difficult to find enlist a helper and go up on the roof with a garden hose.
Isolate areas when you run the hose.
Dig out any cracked or dry caulking that isn t properly sealing adjoining surfaces and replace with silicone caulk.
The tar strip needs to be about 60f to activate.
How to repair a leaky roof from inside the house.
You can t fix a leaky roof from the inside so don t even try.
In the winter a dab of roofing cement or tar should be added to each shingle to bond them together until the tar strip is activated in warmer weather.
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.
Locate the source of the leak by examining the underside of the roof from within your attic or crawl space.
Perhaps placing tube on furnace duct so air heats pre cut tube inside of home then climb up ladder and seal area keeping the sealant warm and easily caulk able.
Start low soaking the area just above where the leak appears in the house.
The shingles can be warmed up with a propane torch.
The secret to caulking in winter time is to heat the sealant in the tube.