If I have a 4 might unit defending at the Frozen Fortress and my opponent plays a Thousand Tail Watcher dealing the -3 might to a minimum of -1, does my unit die?

Yes, your unit will die.

Here is the breakdown of why this happens based on the Riftbound rules:

Sequence of Events

1. Thousand-Tailed Watcher: When your opponent plays this unit, its ability triggers, giving your unit -3 Might. Your unit's Might is reduced from 4 to 1 (as per the "minimum of 1" clause).
2. Frozen Fortress: This battlefield's ability reads: "At the start of each player's Beginning Phase, deal 1 to each unit here."
   • If your unit is at the Frozen Fortress battlefield, it has 1 damage marked on it from the battlefield's ability.
3. Lethal Damage Check: According to Rule 143.2.a, a unit is killed if it has non-zero damage marked on it that is equal to or greater than its current Might.
   • Your unit now has 1 Might and 1 damage marked on it.
   • Since the marked damage (1) equals its current Might (1), the unit is killed during the cleanup check.

Key Rules

• Might vs. Damage: Damage is "marked" on units (Rule 143.3) and does not reduce Might directly. The unit dies during the cleanup check when damage equals or exceeds Might (RiftJudge FAQ #91, #2141).
• Minimum Might: As confirmed by RiftJudge FAQ #91, the "minimum of 1 Might" clause on Thousand-Tailed Watcher only prevents the Might reduction itself from going lower, but it does not protect the unit from death if the damage marked on the unit (from Frozen Fortress) meets or exceeds that new Might value.