I was thinking that a better mini game for taming animals could be something somewhat similar to how the fishing mechanic with the better rod, except with foragable foods and feeding.
The game could be something like this, first you feed it a clover, rope it, then bring it back and attach it to a hitching post. After a few hours, it will be hungry again for food. When you feed it, the taming meter goes up. However, the amount of taming meter increase you get is dependent upon what forageable food you fed it, and what it's random natural tendencies are. So if this particular cow really likes blackberries the best, and you gave it a lingonberry you would only get a marginal increase, instead of the best possible increase.
The numbers and such would have to be fine tuned, obviously, and that would depend on how long you think it is appropriate for the taming game to last, and such. It also might be good for the cows preferences to reset at the 50% mark, however, this also might suck. Not sure.
Either way this game makes more sense, as when you train animals, feeding them (rewarding them) when they do the appropriate thing is almost always preferable to deterrence via pain. So instead of beating your animals into submission you are teaching them through rewards, how to be a cow and such.
Anyway, I think the current game kinda sucks, and that this one may be a better alternative.
Feel free to debate and critique.
Thanks
Ricky