During the Middle Ages, a landowner ( in Finland usually a little wealthier farmer) could be exempted from taxes if he could afford to equip a mounted soldier for military service. Often the soldier was the landowner himself.
I don’t know if a soldier with a horse automatically meant a cavalry man; during long periods of the Middle Ages, battles were commonly fought on foot, and horses were mostly used for transport. In this picture the men are not holding lances, but pole axes, which were infantry weapons.
No doubt the equipment carried by the men of arms varied a lot, and only a few could afford the latest kit.