Does an enemy unit die on Frozen Fortress if I have Elder Dragon in my base?

Ruling

No, the enemy unit will not be killed by Elder Dragon's ability when taking damage from Frozen Fortress.

Reasoning

1. Source of Damage: The ability on Frozen Fortress reads: "At the start of each player's Beginning Phase, deal 1 to each unit here." According to Rule 187.6, the controller of a battlefield controls its abilities. Damage dealt by a battlefield's ability is considered to be dealt by the battlefield, not by you personally.
2. Elder Dragon's Condition: Elder Dragon's ability states: "Any amount of your damage is enough to kill enemy units."
3. Interaction: Because the damage from Frozen Fortress is dealt by the battlefield's ability and not by you, it does not qualify as "your damage." Therefore, Elder Dragon's ability does not apply, and the unit will take 1 damage normally rather than being killed instantly.

Summary of Sequence

• The Beginning Phase begins.
• Frozen Fortress's triggered ability is placed on the chain.
• The ability resolves, dealing 1 damage to each unit at that battlefield.
• Because this damage is not "your damage," Elder Dragon's ability does not modify the lethal threshold. The unit is only killed if the 1 damage is equal to or greater than its current Might.

Note: I could not fully verify this ruling against the retrieved rules.