Yes, although it is not a common problem.
Properly seasoned firewood still has a fair amount of water in it, say 15 to 20 of its weight. That water acts like a regulator of the combustion process along with a few other factors like piece size, load configuration and combustion air supply.
The higher the fuel moisture, the slower the wood breaks down when heated because of all the heat energy soaked up in vaporizing the water out of the wood.
Conversely, the dryer the wood, the more quickly it breaks down when heated. By breaking down, I mean the vaporization of the volatile components of the wood; that is to say, it smokes. The dryer the wood, the more dense is the smoke at a given heat input rate.
Since wood smoke is fuel, we want to burn it as completely as possible and that means mixing with adequate oxygen in the combustion air. The problem is that a firebox load of very dry wood produces far more smoke than the air supplies of stoves are designed to provide. Besides, even if you could supply enough air, you would produce an inferno that would howl in the stove and make everyone in the house nervous. Fires that intense can seriously damage the stove’s innards. Wood that is very dry produces a fire that is hard to control without making a lot of smoke.
Kiln-dried wood is down around 10 percent moisture. Depending on climate and conditions of storage, normal firewood won’t dry down to kiln-dried moisture because of normal outdoor humidity. For example, I’ve never measured wood below about 14 percent in my firewood supply. But I suppose that firewood could get very dry by natural seasoning in desert conditions. Or firewood stored in old barns, which are like kilns in hot summer weather.
The right band of firewood moisture is between 15 and 20%. When you get much over 20% you start to see symptoms of sluggish ignition and the inability to turn down the air without extinguishing the flames. Towards 30% the wood sizzles and fires are very sluggish and it is hard to get a clean burn until the wood is almost to the charcoal stage. Above 30% water bubbles from the end grain when the wood is heated and it is very hard to burn at all. Species like poplar/aspen, which have very high native moisture content are virtually non-combustible when not adequately seasoned.
The main difference between EPA low-emission certified stoves and conventional stoves is that you can turn down EPA stoves for a long burn without extinguishing the flames. That is, they are better at producing a clean, controlled fire. But they are designed for wood that has a moisture content of twenty percent plus or minus one or two percent. Once you go far outside this band, their emission rate goes up. So even the best wood stove’s performance will suffer if the wood is not in the right moisture range.
If you have some very dry firewood, like kiln-dried cut offs or old wood stored in a hot place, mix it with regular firewood to raise the moisture content of a full load.