Equinox will not counter a spell that has a random chance of destroying a land.

Equinox will not counter a spell that deals damage to an animated land, even if it would deal more damage than the land's toughness. This is because the spell itself does not destroy the land directly. The land is destroyed by a game rule.

The ability can target any spell, even one that would not destroy a land.

Equinox will not counter a spell which would indirectly cause destruction of one of your lands.

Equinox will not counter a spell which requires sacrificing land when it enters or one that requires sacrificing land as part of the cost to cast it.

Will not counter a spell which would destroy a land only if a choice is made.

When the activated ability resolves, determine whether the targeted spell would destroy a land if it resolved right then. If it would, then counter that spell. Otherwise, it is not countered, even if the spell could, under other circumstances, destroy a land.