Both is possible regarding the grammar. But they have different meanings. 1) "mir ist kalt" = "ich friere" (Literally: "I'm freezing.") 2) "ich bin kalt" = My skin is cold. But that doesn't necessarily include that I'm feeling cold. 3) "ich bin kalt" = It can sometimes be an abbreviation for "ich bin gefühlskalt" (emotionally cold). In most cases, we use it to talk about other people. Not about ourselves. For example: When somebody isn't crying when something sad is happening: "Du bist so kalt!"

I'd say "Mir ist kalt" describes "how you are (feeling)" while "Ich bin kalt" describes "what you are" for example you are cold in a sense of not feeling any happyness. Or you are a cold blooded killer or maby you are dead ("Er ist kalt"-> no body temperature therfore dead)...ect.