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Check your rain cap. Many times these clog or ice over .
Good luck, let me know how you make out.
I will opt out and allow another expert to help you. I've not dealt with drafting in your climate.
One of two things or a combination of both,
The chimney is being flooded with too much combustion products ( oversize fire ) or there is an exhaust in the home somewhere that is sucking too much air out. let me know if that helps,
Also of the flue is cold it may reverse draft until it heats up,