It depends on your conditions, but sure, you could use all sorts of soil amendments as traction and melting aids.
Char, ashes,
compost,
wood chips, sawdust, black garden dirt. All will work if you have some sunlight or near melting conditions on your driveway.
It's more challenging if you have sheets of hard-frozen clear ice, especially if it's very cold. Not everything will give traction in that case. Sand and gravel are abrasive, giving grip even in small amounts. In the long-ago time, the
ash from coal was particularly helpful -- it's the stuff that grindstones are made of.
The other trick is that you have to have a large supply that is dry and free-flowing at freezing temperatures. A giant frozen block of traction aids that can only be broken up with a jackhammer or dynamite is not particularly helpful.
Edit: Natural materials tend to stick to
boots and track into the house. This leads to a different sort of friction. You may gain traction in one area and lose it in another.