Alvin attacks with Brutal Hordechief and Grizzly Bears. Nate controls two Grizzly Bears, one of which is enchanted by Oppressive Rays. Nate has 3 untapped Forests. Alvin activates Brutal Hordechief's ability. I am confused about what happens next.

Does Alvin have to propose a set of blocks in which the enchanted Grizzly Bears is included? According to the FRF release notes, Nate can veto any such set of blocks that would require him to pay a cost, and Alvin must then propose a different set of blocks. Can Nate just keep vetoing proposals until he is able to block the way he wants? If Nate vetoes every possible set of blocks that includes the enchanted bear, does Alvin then propose a set of blocks that excludes that bear?

Or may Alvin choose to exclude the enchanted bear from the beginning?

While Alvin's able to propose having the Bear block if he wants to, he's not forced to. He can choose to exclude the enchanted Bear from the beginning.