Frigid Touch

Q. If the might of a unit goes below 0 after resolving a Frigid Touch, does the unit die?

No, a unit dies only if they take any damage or if damage marked on them goes higher than their might. So in order to be killed, a unit with 0 or less might must have at least 1 damage marked on it. If the unit already has 1 damage marked, it dies if its might is reduced to 1 or less.