Can second hand cigarette smoke cause cancer? I think the principle is similar.
No one can say for sure if breathing in the smoke from a wood burning stove long term can cause cancer - but if the wood you're burning has been related with pesticides etc... Then it's possible - it's also an irritant - period - is it super smokey? I don't even stand near open outdoor fires anymore - last Time I was someone's house and they got the fire going I spent maybe 2 hours breathing that stuff in and was sick for two days...
Smoke inhalation anyone?

Now I am sure there are many people who deal with stuff like that daily - and have no problem with it - but some people are sensitive to it - so it's an individual thing. My mom was a 3.5 pack a day smoker - she died of lung cancer over 10 years ago - at age 59. Her partner also smoked the same amount - he lived another 9 years - battled colon cancer and won but died from pneumonia - everyone is different.
Hugs.