I will start by saying, I have the luxury of hunting from a wall tent or Tipi every fall. I pack a llama string and that affords me comforts some do without.
With that said, The first thing I do at the end of my day, is disrobe from my hunting clothes and put on my "camp" shoes. Even on dry days I pull my insoles from my boots to let them breathe. Most insoles have a plastic backing that traps sweat. If my boots are damp, I pull the tongue down to really open them and I lay them on their side in the ring of warmth of the stove. Note warmth not heat.
Moist air is more dense than than dry air, so by laying them on their side you are allowing evaporative moist air to flow out of your boot. I rarely have anything but bone dry boots by morning.
I like Dan's Idea of adding warmth inside the boot for drying! Especially for you guys with out access to a stove.
Alaska or the pacific northwest may be a different beast... The mountain west is generally arid. When given a chance things dry very quickly on their own. Most people I know that hunt the Coastal states or Alaska just resign to being wet at some level.