Does heating the air cause the humidity in the air to decrease? Yes and no.

Heating air causes the RELATIVE humidity percentage to decrease, but it does not change the overall moisture content in grains of moisture per lb of air.

Many old-timers will swear a blue blaze that oversizing a furnace will directly result in lower humidity, cracking furniture, etc.

The problem with that theory is that no matter how much you heat the air, you don't change the overall moisture content. Then, when you blow that air into the space, it quickly acclimates to the room.

But there still may be some truth in this oversizing-dries-stuff-out theory.

In the winter, during cold climates, the moisture content is very low outside, regardless of the relative humidity. When you use a larger furnace than you need, you also tend to move more air than you need.

When you move more air, there is often greater negative or positive pressurization of the conditioned space due to zonal imbalance and duct leakage. This pressure imbalance will drive more dry air into the space or more of the inside air out, resulting in lower humidity.

Neil Comparetto also pointed out that when the appliance takes its combustion air from the space, this can cause significant negative pressures, which also draws dry air in from outside. The larger the BTU output, the greater volume of air that must come in for combustion.

The other factor is the supply air temperature itself. If the hotter supply air is blowing directly on an object, it will tend to dry it out more quickly due to the increased temperature of the object itself.

In conclusion:

Furnaces don't reduce air moisture quantity directly, no matter how big or small.

There are other reasons why oversizing can cause issues, so don't do it.

—Bryan