Joaquin823 said:
I mean, the best archer in your army should stay an archer right?
No, not in this time period. These aren't professional archers of later eras--they are peasants who picked up their hunting bows as the weapon they could bring to battle, as others picked up what they had available. And just as the freeholders who picked up a spear has hope of a greater role as he gathers equipment from loot and pay, they do as well.
This is especially true for the Norse, where the bow was used widely by many warriors, likely without much actual distinction or idea of an "archer" as a seperate role: http://www.hurstwic.org/history/articles/manufacturing/text/viking_bow.htm
Joaquin823 said:
I think the same would apply for horsemen.
No, this is not strange at all given this time period, because in the background, your highest level units very likely are riding around on horses as well, except during combat, even all those high level Norse units, despite lacking any cavalry, also likely have horses. The first thing the Great Heathen Army did on landing is acquire horses from East Anglia, and that was standard practice for invading Norse armies, raid or threaten to get horses as soon as they step off the boats: https://en.wikipedia.org/wiki/Great_Heathen_Army . Warriors widely rode horses in this time period, they just preferred to fight dismounted.
So what is happening when a light cavalry soldier upgrades? Well, he acquired mail armor during one of those post battle loots, or bought it with spoils from loot and the pay you give him, and happily ascended to a more prestigious role, fighting as warriors do at this time, riding his horse to battle and then dismounting to join the shieldwall. This was almost certainly a more prestigious role for him, with greater opportunities, than continuing to serve as a scout and such in the light cavalry role.