The axe was a very versatile weapon in combat, and it’s likely that any status fighter could have one. From the farmer that has grabbed his wood chopping axe to the Huscarl swinging his Dane axe. There are various types of axe, the wedge axe is a wood chopping axe and would have been used by lower status fighters, you then have a thinner battle axe that would have been used specifically as a war axe, and these were thinner with more of a piercing head to cut through armour. You then have the Dane axe which was near a pole arm, they had a broad head on a long shaft and would have been used by the highest status warriors in mail, and due to not being able to have a shield, mail would have protected them.

Examples of Axe finds

Beorhtric wielding a dane axe on the field of Hastings