I couldn't explain the physics behind it, but I can attest to the dry air when we use the woodstove.
We have a fairly airtight house (built in 2003/2004), but also have a fresh air ventilation system as required by Washington state building codes. So we always have fresh air entering the house.
The woodstove has it's own external air supply and doesn't take air from our living space.
It's not too bad if the weather is rainy, but if it's a cool dry day, it only takes a couple of hours before our noses start feeling dry, and we start getting lots of static shocks.
Our small woodstove puts off way more heat than we need to heat up the house comfortably, so a little heat loss to evaporate the water is a minor issue. I doubt blocking a small 6"x9" area on the top of the stove is going to make much difference anyway, since a lot of heat seems to come from the front and sides.
We only use our woodstove for supplimental heat. Mostly for the romantic aspect and for power outages. A cord of wood can last us almost two years. I'm not too worried about using a little extra firewood.
Anthony