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Estar com frio vs. ter frio

Both estar com frio and ter frio describe the sensation of feeling cold. The primary difference is regional preference: estar com frio is the standard in Brazilian Portuguese, while ter frio is the standard in European Portuguese. Grammatically, one expresses a temporary state (estar), and the other expresses the possession of a sensation (ter).

Estar com frio

A1
This phrase literally translates to to be with cold. It uses the verb estar, which indicates a temporary condition. It is the most common way to say I am cold in Brazilian Portuguese, focusing on the current moment.
Estou com frio agora.
(I am cold right now.)
Você está com frio?
(Are you cold?)
Se eles estiverem com frio, feche a janela.
(If they are cold, close the window.)
Nós estamos com muito frio aqui fora.
(We are very cold out here.)

Ter frio

A1
This phrase literally translates to to have cold. It uses the verb ter. In European Portuguese (Portugal), this is the standard way to say you feel cold right now. In Brazilian Portuguese, this form is rarer and can sometimes imply a permanent characteristic, like being a person who always feels cold.
Tenho frio nas mãos.
(My hands are cold.)
Ela tem frio sempre que chove.
(She feels cold whenever it rains.)
Não tens frio sem o casaco?
(Are you not cold without the coat?)
Os cães também têm frio no inverno.
(Dogs also get cold in the winter.)

Summary

To sound natural, use estar com frio if you are speaking Brazilian Portuguese and ter frio if you are speaking European Portuguese. While both are grammatically correct, estar com frio emphasizes a temporary state you are with, whereas ter frio frames the cold as a sensation you have.