kate,

Any organic matter will loosen up heavy clay soil. Leaves, cow manure, chicken manure, anything organic will do it.

Heavy clay soil itself is full of nutrients. Much better than sand. It also holds moisture better too. Just don't put sand in heavy clay.

Just don't put sand in heavy clay.
Unless you want to try to make some lovely orange adobe bricks. ; P
And re Heavy clay soil itself is full of nutrients: not just because they had them; the clay holds on to those nutrients so that they aren't easily washed away. But the binding may bring up the pH of that soil because the wrong pH might allow the clay to hang on too strongly and fail to release those nutrients. I therefore suspect that correct pH may be more important in clay soils than other media.

Just an update for anyone interested--we did use the cotton soil and it mixed well with the clay and loosened it up nicely. Sometimes we had to pull gin junk out of the soil, but that was easy, because the "junk" consists of hunks of cotton. We put the hunks of cotton in the woods for birds, etc. to use for nest-building.