Cold air supports less humidity than warm air. Cold air drawn into the home becomes warm. Though it has the same amount of water, it can "hold" more than before. Thus the "relative humidity" drops significantly. That cold outside air which was at 55% humidity can easily become 10% inside your warm house.
Solid fuel stoves suck up lots of air from your home and send it up the stack. Outside air comes in every crevice and crack to replace it. Molds and bacteria generally love humidity. Viruses are stabilized in dry environs. Furniture, flooring and people like it between 30-70%.
Humidifiers are a great solution to the problem. You have a few choices: free standing and central. The freestanding units use heat, water soaked pads, or ultrasonic mists. Hot units emit zero viable molds, viruses, or bacteria (but their "dead" proteins can still be allergenic). They cost the most to operate. Filters and pads are subject to hard water problems and can breed microbes. Maybe true for ultrasonic too, but they tolerate hardness somewhat better.
Central units are a different animal. I agree with the other member who cited problems with them.
I have (or have had) all of them. The hot unit is great with a sick stuffy kid, but costs too much to run for daily use. The corrugated pierced pad type hardened up with lime from my well water too fast for my liking. I also have one with a little pump and a metal screen. The screen has silver (or something) to inhibit bugs. It works fine and resists lime, but its fan/pump is a bit loud. The ultrasonic is my favorite: silent, puts out moisture, low energy consumption, tolerates hard water (but can leave dried lime "dust" around it which cleans up easily.
My central unit was an aerosol type and left puddles in my ducting. Besides whatever grows in that, it starting rusting the ducts.