I answered a question on a somewhat similar topic a few months ago

Edit: the study referenced in the comment this links to actually measured CO2 (as pointed out by u/imjusthereforrecipes), not smoke particulates. I didnt read the article in depth enough (for which I apologise) and it honestly is baffling to me that CO2 was what they chose to measure instead of the smoke levels.

I can't answer with regards to Scottish blackhouses specifically, but there is a wide array of literature documenting the harmful effects of burning biomass for fuel (usually for cooking) in the developing world today. It's implicated in a variety of lung and other health problems.

For example this paper: Effects of cooking fuel smoke on respiratory symptoms and lung function in semi-rural women in Cameroon finds

Our results indicate that the main respiratory symptoms related to using wood as a cooking fuel were dyspnea on exertion and chronic cough suggestive of chronic bronchitis. In addition, we found 2 cases of COPD and 13 cases of restricted lung function. We also demonstrated a statistically significant association between reduced FEV1 and the type of cooking fuel, chronic bronchitis, age, and height

Similarly, this paper shows a reduction in respiratory illnesses in children in households where cooking occurs out of doors.

Now, both of these focus on wood rather than peat, because heating with wood is much more common today, but peat smoke from wildfires is also associated with health problems.

I think it's clear that breathing in peat smoke would be unhealthy, regardless of the place or time.