To keep humidity in the house, rather than adding water to the air, keep the already moist air from leaving. Heating the air doesn't make the water go away, it changes the relative humidity.
If you find that your house dries out excesively when you run the stove, your house is probably venting the warm air out the top (attic hatch sealed?), and drawing in relatively drier, cold air below. This air change is called stack effect, and can also cause chimney reversal (may other things do too, like bath fans dryers and range hoods)
We had the driest house I have ever experienced last year (first winter in new 75 year old house) - humidity guage said "LOW" from October to April, coincident with the heating season. We were not burning wood at the time.
This summer we did some energy refits based on an audit we had done - new windows upstairs, R 60 in the attic, sealed the attic hatch, and things were better. Then, finally, our window contractor recieve the basement windows (2 windows, 1 ft x 2 ft approx) and got them installed. That was the day we noticed the climate in the house change. The old windows, you could see around the frames from rot, and the basement was always cold.
Get some caulking or spray foam, and start sealing around the sill plate of your house, caulk the basement windows, and caulk the attic hatch shut (assuming you don't need up there regularly) That air sealing will keep the air you heated in the house, and hence the moisture in the house.
I am actually a little worried that I will need put in a vented range hood now, cause it feels like London Fog in the house when ever we boil spaghetti - definately didn't have that problem last year.