2 archers and 2 inf
vs.
2 inf and 2 cav
infantry players fight with each other, 2 cavalry handles 2 archers with ease. Even if archers can shoot back, horses don't die in 2-3 shots that easily.
Tactically, I believe the archer group has the advantage in most situations.
If there's any sort of distance between the two groups, the archer group would win, due to the initial damage output from the arrows. It would take a good 20 seconds+ for the melee group to even get there, allowing the melee to repel the cavalry up close. Whoever's melee group wins also wins the fight, and the cav won't be helpful against melee until the melee groups are fighting. The archers can also focus on the melee and allow the infantry to dispatch the cav if they don't get off their horses. If there are any props that provide cover at all, even a simple wall, the archer group also has a higher chance of winning. If both teams are wounded prior to the engagement, the advantage is heavily favored towards the ranged group even more.
I could imagine your example only working on an open field when all 4 players are already very close to each other. The non-ranged group can win in the other disadvantaged situations only if the cav are better players.