In describing living creatures English is ambiguous. Even if we leave aside possible figurative meanings, “you are cold” may signify either that you are externally cold when someone touches you-cold in the sense that an inaminate object is cold- or that you feel cold to yourself internally. There appears to be no way to remove the ambiguity short of using an explanatory phrase; “you feel cold” still has two possible literal meanings. As we shall see some other languages are not ambiguous on this point.
Source: Adjectives of temperature by Clifford H Prator, professor of English, University of California
I would like to know whether the sentence “You are cold” is really ambiguous as the professor claims.I do not like or sound to be controversial
Yes, the English language really is ambiguous in this point. It’s clear that the predicate “be cold” has multiple meanings in English, as described in the question: I can say “This plate is cold” to mean that I feel a sensation of cold when I touch the plate (the plate causes people in contact with it to feel a sensation of cold), or I can say “I am cold” to mean that I feel an internal sensation of cold. The structure of the predicate is the same in both cases (a form of “be” + the adjective cold). (Cold also has other meanings, like a metaphorical meaning when applied to interpersonal relationships, or a less subjective meaning related to the scientific definition of temperature.)
The comments below your post seem to be focusing on whether there is a substantial risk of misunderstanding. There isn’t (in general), because there isn’t much overlap between times when we want to describe an object that is cold to the touch and a person who is experiencing the sensation of cold. But the fact that context or tone of voice can make the meaning clear doesn’t mean that this part of the English language is not ambiguous. If it were unambiguous, you wouldn’t need context.