You could do, but I would not because they take ages to rot. Put them in a corner and forget about them for a year or two.
I would be inclined to discard them and although the smell is awful I would burn them because if the wind is in the right direction the nearest house is miles away, so no problem.
You could keep them until the spring and then put out in a net or similar for the birds to use for nest material.
Of course you could give the old pillow to a charity shop or somewhere similar.