@Kjertesvein nothing was requirement and personally i think they didn't use fur in battle. But since they are highlanders they have been using fur up to the modern days.
If you didn't like the fox on the shoulders then i get it. If you dig in the paintings you will find more inappropriate things. But they were just his paintings and nothing more. What he was claiming does have verifiable evidences which you can find in the old thread.
Talking about Tadzreuli, you should note that they were nobles. There is only one maybe two miniatures where Georgians have axes. And in all other frescoes and miniatures they have swords or maces. Also since they were nobles, according to written sources, they mainly, if not only, used swords and maces. Axes were used by non-nobles.