Everything in Wesnoth -- hexes, units, villages, time, gold, etc -- are abstractions for a battle that is taking place. They will inevitably fall apart if one over-analyzes them.
Do you really think that if you capture a village at midnight, it'd have paid you some gold in taxes by dawn? Can one guy really capture a village? Why can't more than one guy be in the same hex, since hexes are obviously pretty big? Why can a castle only fit eight guys in it? (Especially since it covers many square miles!) Wouldn't your units collapse from exhaustion after 96 hours of straight fighting?
Anyhow the answer to how large hexes are is simple: they are one league across.
“At Gambling, the deadly sin is to mistake bad play for bad luck.” -- Ian Fleming