I can trade items to my non-hero units. Click their portrait circle so they are selected, and then click the "Trade Items" action in the tab to the left.
The problem I am having is that although my non-hero unit can carry the items I trade to them, they cannot use them. That is, it appears that once I have trained a soldier unit, for example, they are stuck with the equipment they had when trained. I also cannot unequip their items as I can with hero units. I guess this makes sense in that if I trained a peasant with a club, he can't use a sword later. All he knows is how to wield the club.
So the non-hero units can carry items back and forth to give them to heroes or your sovereign in the field, but they can only use the weapons and armor they had when trained.
I've only played the campaign, though, so I've not got the best experience with the game. Maybe the campaign is restricting options for its gameplay purposes.
Maybe there is a tech later that will cause updates to go out to all your military units immediately. I saw a loading screen tip that indicated that's the way it works with building upgrades like huts to houses.