If the trigger of frozen fortress is not announced by either players at the beginning phase, will the damage later be applied to the units?

No, if the Frozen Fortress trigger is not announced and acknowledged by the accountable player, the damage will not be applied to the units.

According to Tournament Rule 506.3, the accountable player must acknowledge their triggers by the time they would have an observable impact on the game. If they do not, the trigger is considered forgotten.

Rule 506.4 explicitly states: "A triggered ability that was forgotten never goes on the chain."

Key Details:

• Accountability: As per Tournament Rule 506.1.a, the accountable player for triggers sourced from a battlefield is the player who currently controls that battlefield. If it is uncontrolled, it is the current turn player.
• Observable Impact: Dealing 1 damage to units is an effect with an observable impact (as it affects unit health and potential survival).
• Result: Once the game has progressed past the point where the damage would have occurred (the Beginning Step) and a new game action is taken, the opportunity to place the Frozen Fortress ability on the chain is lost for that turn. The units will not take the damage later.

If the controller of the battlefield simply missed the trigger, it is treated as a "missed trigger" under the tournament rules (Rule 506.3.b/c). It does not "fire" retroactively later in the turn.