The important thing with any leather derived product, is to dry them carefully and slowly, preferably in a cool temperature.
Never force dry them, such as near a heat source such as a radiator or warm fire.
A careful polish with a quality wax, will certainly do them no harm, but just ensure the boots are cleaned properly and dried properly.
If you get this right, then a good pair of leather boots can last quite a few years.
I always look at the legendary climbing boots used by Sir Edmund Hillary in his conquering of Everest, inside the Pen Y Gwryd below Pen Y Pass.
They sit inside a glass display case, alongside a length of rope he also used going to the summit.
The boots, made of leather, are in remarkable condition, because they have been well looked after