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So far it sounds like an improper sewer vent installation. In cold weather the air outside is more dense than the air in the house and it will 'fall' or draft down the vent into the plumbing and bypass the sink and tub traps. That is an educated guess, likely no more than 70% chance of being correct.
More likely is a sewer vent not run through the roof, but terminated in the attic, of not connected properly in the wall.
Another more likely cause is a 'dry trap' any unused sink will result in the trap below the sink drying out over a few weeks time, if that happens sewer gas will have a direct pathway to the inside of the house.
Let me know what you can discover, we can go from there.