If my limited knowledge of the subject is correct Grenadier's companies or battalions were issued with the mitre cap so as not to obstruct the throwing of Grenades, which the old Tricorn caps did.

A bearskin, was issued, post Waterloo, to comemorate the defeat of Nappoleons Gaurds at Waerloo.

Walrus, can you comment ? - Sorry I'am better at naval history for this era.