Does Frozen Fortress trigger even with no units on it? So, would you be able to use the trigger to react and use a spell or reaction speed ability?

Yes — Frozen Fortress triggers even with no units on it, and that trigger creates a full reaction window for both players.

The trigger condition is purely temporal ("At the start of each player's Beginning Phase" — Rule 383.1), with no requirement that a unit be present. When the Beginning Step arrives, the ability is placed on the chain regardless of what's there (Rule 383.3). Putting it on the chain puts the game in a Closed State, so either player can play Reaction-speed spells or activate Reaction abilities before it resolves (Rule 813, FEPR Execute step). When it finally resolves with no units at the battlefield, the "deal 1 to each unit here" instruction simply does nothing.

One practical note: since the ability has no observable impact when the battlefield is empty, under Tournament Rule 506.3 the accountable player (battlefield controller, or turn player if uncontrolled) should still acknowledge the trigger if they want that reaction window — a forgotten trigger never goes on the chain (TR 506.4).