How to get smoke out?????????

i have a wood stove down in my basement and i just bought new aspestus rope and i noticed when i went down in the bastment i saw smoke coming out of the doors my home is relatively old its 37 years to be exact but i checked the flue its upright to burn the knobs on the doors are giving it oxygen but i went to check the door on the chimney and theres snow in it could the snow be causeing this???