One concern is that smoke can suppress macrophage function, altering it enough that you become more susceptible to respiratory infection. A colleague who looked at lag time in the effect of wildfire smoke exposure found an increase in influenza cases after a bad fire season. Studies in developing countries have also found increases in respiratory infections with people who are cooking on open fires in homes.
The stress of an inflammatory response can also exacerbate existing health problems. Being exposed to wood smoke won’t independently cause someone to have a heart attack, but if they have underlying risk factors, such as significant plaque buildup, the added stress can increase the risk.