You could say: "Yesterday, the temperature for Brrr, Minnesota, dropped below its historic minimum." Or, "dropped below its average minimum for the past N years."
That's two words and you asked for one word. Sorry. Even if you use recede, you will have to say: "Temperature for Brrr receded below its ......" as BleepBlopOverflow's answer said.
You are right in thinking that Exceeded the minimum is going to be interpreted as that the temperature was above the minimum. Possibly you could make an argument the other way, but it would be a hard sell. If you want clarity, don't say "exceeded the minimum" when you mean "below the minimum".
Exceed:
be greater in number or size than (a quantity, number, or other
measurable thing). "production costs have exceeded $60,000"
•go beyond what is allowed or stipulated by (a set limit, especially
of one's authority). "the Tribunal's decision clearly exceeds its
powers under the statute"
synonyms: be more than, be greater than, be over, go beyond,
overreach, top "the cost will exceed $400"
•be better than; surpass. "catalog sales have exceeded expectations"