When does the player who plays Carnivorous Snapvine select the enemy unit, and can opponents react by buffing their unit once it's targeted?

Ruling: Carnivorous Snapvine's on-play ability is a triggered ability that goes on the stack/chain when Snapvine is played. Players can react to this ability while it's on the chain (for example, by using Stupefy to reduce the unit's might). However, you cannot counter the ability directly with cards like Defy or Wind Wall, as those specifically counter spells, not unit abilities.

Sequence:

• Snapvine is played
• Its triggered ability goes on the chain
• While on the chain, players can react to it
• The ability resolves

Nuances:

• If Snapvine is played during end of turn (such as via Dazzling Aurora), reactions can still be played in response to the Snapvine trigger, but once the trigger resolves and the chain empties, the end step continues normally with no window to play actions
• You can also react to the Aurora trigger itself before Snapvine's ability goes on the chain