A furnace that uses a vent system to exchange used air with fresh is continually bringing dry air into the house. As the furnace engages in a combustion reaction, hot, wet air is vented out of your home. The intake then draws in air that is cool but which is also likely drier due to the winter conditions outside when most furnaces are running. This has an eventual drying effect on the air in your home.
If the ducts in your house are not properly sealed, the effect of cold air being drawn into your house will be magnified. Leaks in the duct system creates a type of vacuum that continually draws the dry, outside winter air into the home. Not only will this dry out the air in your home, it will also decrease the efficiency of your heating and increase your energy costs.
Not all types of heating dry the air as much as a forced air furnace system does. Radiant heat, for example, does not rely on the constant circulation of air the way that a forced air system does, so the humidity tends to not be affected as adversely. Heat pumps also don't dry the air the way that other types of furnaces do.
If you don't want to have to resort to small, portable humidifiers that are rolled from room to room, look into a furnace with an incorporated humidifier. These condition the air as it is sent into the ductwork. This ensures air with an acceptable level of humidity that is smoothly sent throughout the entire home. This is difficult to achieve with stand-alone units.