Does Fateful Hour apply in this combat?
Dealing damage does not directly destroy creatures. It's actually state-based actions performed afterwards (the next time someone would get priority) that do. His Grizzly Bear would survive because your opponent has 5 life when SBAs are performed.




All participants assign their damage [CR 510.1]. No damage is actually dealt at this point, so your opponent has 7 life for the entire process, so his Grizzly Bear is 2/2 for the entire process.


2 damage is assigned to your blocked attacker by his Grizzly Bear
2 damage is assigned to his Grizzly Bear by your blocked attacker.
2 damage is assigned to him by your unblocked blocked attacker.

All participants deal the previously assigned damage simultaneously [CR 510.2]. (The power/toughness of the participants is not checked here.)


2 damage is dealt to your blocked attacker by his Grizzly Bear.

2 damage is marked on your blocked attacker.

2 damage is dealt to his Grizzly Bear by your blocked attacker.

2 damage is marked on the Grizzly Bear.

2 damage is dealt to him by your unblocked blocked attacker.

He loses 2 life.


State-based actions are performed.


Your blocked attacker is destroyed because its toughness, 2, is not greater than than its marked damage, 2.
(Nothing happens to his Grizzly Bear because its toughness, 6, is greater than its marked damage, 2.)
(Your opponent does not lose the game because his life, 5, is greater than 0.)