In the early and high Middle Ages these animals were of the lord. A farmer that worked a large field could be entrusted with a cow or two. These would provide milk and heat for the farm. All other cattle were under the worked by a cattle herdsman. When needed a pair of oxen would be taken out of the herd to pull carts, aid in construction or to plow field.

So for most if the year a typical farming peasant wouldn't have access to a ox, not even mentioning the royal and graceful horse. The system of ownership was basically the same a with the fields and farmyards.

In the later Middle Ages the farmers grew 'richer' so personally owned cattle and even horses started became more widespread.