Can you kill a unit with Frigid Touch?

No, you cannot kill a unit using only Frigid Touch.

According to RiftJudge FAQ #80: "No, Frigid Touch alone cannot kill a unit. Units die only when they have nonzero damage marked on them that is at least equal to their Might, so it always takes at least 1 point of actual damage to kill something."

Additionally, Rule 410.1.c states: "A Stunned Unit must still have damage applied to it equal to, or greater than, its full might value to be killed." While Frigid Touch reduces a unit's Might, reducing Might to 0 or below does not kill a unit by itself; the unit must still have damage marked on it that meets or exceeds its current Might value.