According to the article, while oak is best - for durability, but it is expensive. - and it does tend to warp, shrink and split. Most of our fencing is oak, some of it very old, but it does shrink from the ends - lengthwise, which means even if the board itself is still ok, it no longer reaches properly. Also it is damn hard, which means almost impossible to put a nail in, so you need to use wood screws, and a screw driver.
Dwayne Job in the article does recommend ash as an alternative, and he also recommends using an electric wire to help keep the horses off the fence.
OP, I would think if you have the ash, and it is usable, you should use it. The price of wood is so high right now, I think people would be glad to have the alternative available.