try walking on your heels or toes. it worked for me

As Buckboy touched on, walk heel to toe, you'll sound more like a hoofed animal. walk as deer walk, 2 or 3 steps then observe your surroundings, then continue. You learn to walk quietly and give your self time to pick your path and check for game. You can try soft fuffly or leather house shoes/moccasins, these will allow you to feel the twigs will be more stealthy than rubber boots or hutning boots.

Hard to sneak in on a deer. If they're in the area, they hear you. The turkey call trick puts them at ease a bit, but you still gotta be as quiet as possible. I try to walk without stopping, and they'll let you walk right by. If you stop, they get nervous and bolt.

Not much you can do but wait for a rainy day. Hunt mostly in the early mornings when the conditions are dry like this. If it is cloudy at night, often the dew is not that great in the morning. Watch for the clear nights that cloud up a few hours before morning. That will give you the cold you need for dew but also limit the amount of moonlight. Once the heat is on in the middle of the day or in the afternoon, forget about moving around much. Put yourself in a place where you can see things moving around at dusk without moving yourself.

It's the body weight that causes the noise, not the surface of the boots. Can't see how wool socks would help much. They would, however, get caught on every twig and leaf underfoot. In short order they'd be tatters. Sounds hazardous to me. I wear wool gloves when hunting and usually can't get a pair to last through the season before they're rags.

You can roll step or just very gently place your foot flat on the ground kind of like you are stalking and that does not make much noise.