There isn’t a reliable single count for “cars released with wooden axles,” because that detail shows up in a few very early, highly specialized vehicles rather than in a broad production category. One clearly documented example is the 1907–13 Brush, which is described as having wooden frame and wooden axles.

If you meant production cars made with wood in their bodywork , that is a different question: Ford reportedly sold around 10,000 station wagons with wooden bodywork in 1940, out of over 500,000 cars produced that year. If you meant a specific make or era, I can narrow it down.