H.A.F.
a.k.a. Rusty Nails
But since it is not actually freezing the roots, I am guessing that this is not like a nute lock-out - and would completely fix itself after the ice melts. Unlike having nute lockout.The freezing temps are what cause lockout. Drowning roots would work as you described yeah, but would only be ok short term because at somepoint the plant would just drown I would think.
drowning = shut down root system
Freezing = lockout
I can see the drowning part being an issue if you kept it on for a few days so that's a great point, though I think the constant moist soil and not the temperature would be the primary villain.
I think that for a one-time, "let the ice melt and call it a watering" treatment it is definitely not an issue right before harvest. As long as you let the soil dry before the next regular watering I don't see how it could be that harmful mid-grow.