Unexploded Cows placing into another player's herd
The rules I found here state:


  On your turn, you may rearrange your field as much as you want.
  However, you can not rearrange someone else’s field, so when you
  play a cow on someone, it must go at either end of the line (your
  choice).


So, whoever plays a cow on someone else's herd, they decide on which end it goes.