Bighorner Rancher’s second ability is a mana ability. It doesn’t use the stack and can’t be responded to. If the greatest power among creatures you control is somehow 0 or less, no mana is added.

The amount of life you gain from Bighorner Rancher’s last ability is determined when the ability resolves. If at that time the greatest toughness among creatures you control is 0 or less (probably because all of your other creatures were destroyed or otherwise left the battlefield in response), you won’t gain any life.