[koolba]

Barring a completely incorrect install, the exhaust of the furnace should be completely vent out of your home. The indoor air is warmed by passing against a heat exchanger.

If you’re having issues with air quality have your humidity levels checked. If it’s too low, a furnace attached humidifier will solve that by adding humidity to the treated air.

[RHSeeger]

We have a fairly new forced hot air heating system, and it has a humidifier in-line. It's amazing. You don't really notice it so much until you don't have it. When I'm in a house with forced hot air that doesn't have it, I find it painful. I was at a hotel in DC a while back that had the air on all evening, and my eyes hurt fiercely, dry due to the air. I don't get much of that at home (I'd get none, but... my eyes are broken enough that they're constantly dry to start with).