Growing up and living in Texas, I've visited Mexico quite a bit in my life. From trips to border towns, to the beaches of Cancun, Playa del Carmen, and Cabo san Lucas, and even multiple cross-country car trips to the deep interior. There's a commonality among all those places, and it's that both the air conditioning, and the refrigeration, are typically just sort of "cool." Not really cold, just something slightly cooler than warm.
I coinced a term for that, I call it "Mexicold."
European air conditioning tends to be the same. It can take the edge off, but ultimately, it's just Mexicold.