The corinthian helmet on horseback?

[hoplite14gr]

The Corinthian surely could and was used, but Xenophon (art of horsemanship) advocated against closed helms for cavalry:

[3] For the helmet we consider the Boeotian pattern the most satisfactory: for this, again, affords the best protection to all the parts that project above the breastplate without obstructing the sight.

Correct. Yet we see from art that the Thessalians and Macedonians following Xenophons advice but the chalcidic, attic and thracis helmets remained in use in the late classical to Hellenistic times

Kind regards