Frío vs. frialdad
Both frío and frialdad relate to low temperatures, but they serve different grammatical and descriptive purposes. The word frío is the common, everyday term used as a noun for the temperature itself or as an adjective to describe something that lacks heat. On the other hand, frialdad translates specifically to "coldness" and is a noun used to describe the inherent physical quality, state, or penetrating nature of a low temperature in an object, space, or climate.
Frío
The word frío functions as both a noun and an adjective to express the everyday physical sensation of low temperature or the actual lack of heat in a person, object, or environment.
Hace mucho frío en esta habitación.
(It is very cold in this room.)
Tengo frío porque olvidé mi chaqueta en el coche.
(I am cold because I forgot my jacket in the car.)
El viento frío soplaba por la ventana abierta.
(The cold wind blew through the open window.)
No me gusta el frío del invierno en esta ciudad.
(I do not like the cold of winter in this city.)
El café ya está frío y no sabe nada bien.
(The coffee is already cold and does not taste good at all.)
Mañana habrá un frío intenso en la cima de la montaña.
(Tomorrow there will be intense cold at the top of the mountain.)
Frialdad
The noun frialdad means coldness and is used to describe the physical quality, persistent state, or penetrating nature of a low temperature found in an object, physical space, or climate.
Me sorprendió la frialdad del suelo de mármol bajo mis pies descalzos.
(I was surprised by the coldness of the marble floor under my bare feet.)
La frialdad de la cueva nos obligó a salir rápidamente.
(The coldness of the cave forced us to leave quickly.)
Siento la frialdad de la noche entrando por las rendijas de la puerta.
(I feel the coldness of the night entering through the cracks in the door.)
La repentina frialdad del agua del mar lo asustó al saltar del barco.
(The sudden coldness of the seawater scared him when he jumped off the boat.)
Es muy difícil acostumbrarse a la constante frialdad de este clima nórdico.
(It is very hard to get used to the constant coldness of this Nordic climate.)
La frialdad de las paredes del castillo era evidente al tocarlas.
(The coldness of the castle walls was evident upon touching them.)
Summary
In summary, use frío for the standard physical sensation or measurement of a low temperature, whether as a noun or an adjective. Choose frialdad when you want to specifically highlight the descriptive quality, atmosphere, or penetrating state of "coldness" within an object or environment.