Assassin:
Best for Critical Strike and Freeze Builds: While typically associated with Path of Exile 2 Currency poison builds, Assassin is a powerful Ascendancy for cold builds that rely on critical strikes and freeze mechanics.

Ambush and Assassinate: This ascendancy increases crit chance and crit multiplier, which is incredibly useful for cold builds that rely on critical strikes to freeze enemies more reliably.

Ambush provides attack speed while Assassinate boosts damage dealt to critical strike enemies, which is beneficial for both single-target and AoE cold attacks.

Noxious Strike: This increases both cold and poison damage, making Assassin a strong choice for hybrid cold/poison builds.

Assassin is great for high burst cold damage and critical strike-based freeze builds.

Trickster:
Best for Hybrid Cold Builds: The Trickster Ascendancy offers more defensive capabilities and mobility while still boosting cold damage.

Swift Killer: The Swift Killer node increases cold damage, especially for cold attack-based builds, as well as improving attack speed, which synergizes with cold crit builds.

Ghost Dance: Trickster's Ghost Dance provides evasion and energy shield regeneration, which is great for survival and tankiness while maintaining solid cold damage output.

Patient Reaper: Grants life regeneration and boosts damage over time, making it ideal for cold DoT builds that focus on applying chill and cheap POE 2 Exalted Orbs freeze effects over time.