This is complex...

Hot air can hold a lot more moisture than cold air. (what you said). However when you take cold air and heat it the amount of water in the air doesn't change, while the amount of water than the air can hold did. When talking about water in the air the important part is how much it can hold relative to how much it does hold, not how much it actually is holding.

What we concern is relative humidity so heating air drys.

I think what is more true is that typical furnace designs remove moisture from the air that they heat.

Most comfortable place I ever lived in, heating wise, was an old house that had been converted into apartments. It still had steam heat. I loved that.

A furnace doesn't remove moisture.

Steam heat is radiant which feels very good. Nothing to do with moisture added, steam heat is almost always a closed loop so no water is put into the air.

1-pipe steam has to have vents at the radiator which do let a small amount of water vapor into the room (despite being mostly closed loop). 2-pipe steam does not have this limitation.

Maybe modern steam heat doesn’t, but the vintage system in that house did let some steam out. But even without that, it didn’t drop the humidity like forced air heating does.