Re: eczema treatments and dry winter skin??
Eczema is often tied to allergies/sensitivities, but not always. One of the biggest culprits in our house is dairy. More specifically, it seems to be lactose, as we're all fine on raw milk. Anyway, we are also careful about soaps and detergents. You may have to play around with those some. And don't assume that because it says "free and clear" that it'll be okay.
Now, what we found to work best on eczema breakouts is calendula cream. Children don't get bathed but a couple times a week, unless they are really dirty. We use coconut oil as a moisturizer. Cooler water is better, and oatmeal in the bath water can help with the itches. Drink plenty of water and add good fats into your diet. We take fish oil to help with that.
For your hands, try to avoid water as much as possible. Wear gloves, for instance, when doing dishes. For your face, I would recommend you look into the oil cleanse method. It cleanses and moisturizes, and since you mix the oil yourself, you can easily tweak it back and forth for when you need more moisturizing and when you need less.