I have a cool air, since warm air breeds bacteria, and my home is is really dry and hot.
I can't answer your question, but I can tell you from experience that I can't tell a difference with using a humidifier vs not using one. My kids were sick last month and it didn't seem to help at all. In fact, my DS still has a runny nose and congestion and its been over a month. Doctor says he's fine otherwise though. The runny nose is just lingering.
My thought was the humidifier itself is the cause of issue, not the moisture in the air. We just keep water on the wood stove to keep the air moist. On really cold days I can be putting more than a gallon of water a day into the air. I don't know it is healthier, but our skin is less dry and we don't have such static electricity issues! Plus I put cloves, cinnamon, orange peel, etc in the water so it smells great!
The problem is that humidifers are a breeding ground for bacteria. You can cut the risk of that by using a cool air humidifier, using distilled or boiled water in it only, and cleaning it with vinegar or bleach on a daily basis. We've found it didn't help much for my asthmatic so I just threw ours away. My parents use a cast iron kettle in their fireplace filled with tap water to add humidity to the air though and haven't had any issues since they are boiling it essentially. A pot on a woodstove would be fine since it's boiling the water to add to the air. But a mechani*ed humidifer just tends to breed bacteria.