Wood smoke is a mix of toxic chemicals, not unlike cigarette smoke. Whether it be a tent, yurt, tipi, or some other small shelter, I personally don't care to expose my lungs to it anymore than is necessary. A friend who was a chimney sweep, and never smoked a day in his life, died from lung cancer at an early age, most likely from breathing the dust from the chimneys he cleaned.
Another friend had a hospital supply business, which included supplying oxygen concentrators to people with breathing problems. The concentrators pulled room air through a filter, and then increased the oxygen level through some process. He said that whenever he went to a house with wood heat to service the concentrator, the filters would be black. This was in houses with airtight woodstoves and good piping. The simple act of opening the stove door to feed more wood caused a momentary puff of smoke to enter the homes. Over time, especially in Winter, when people try to keep their homes sealed up as tight as possible, that little bit of smoke would build up, contaminating the inside air the house.
Many years ago, I heated with wood heat using a high quality wood burning furnace. By the end of the heating season, you could write your name in the gray film that developed on the Tupperware plastic. After that experience, I said no more wood heat.
I am not terribly worried about the small amount of time I spend in my hot tent, but I try as much as possible to avoid breathing wood smoke at all costs.