Is it natural to say "Me, I xyz"?

I've never heard a native English speaker say this unless answering a question ("Who wants lunch?" "Me, I want lunch!"). I think it's fine to do what you do in Spanish too. Using "as for me,..." would work well, but it's unusual and formal (at least in my dialect). In informal speech, I would probably omit the "as" and just say, "For me,...".

This sort of reply is acceptable in the locution "me too" (Me too, I'm cold.) but otherwise it does not appear to be idiomatic. This is not found in print (ngram). "Me I am" yields just one result, the title of a book and this is probably not the expected syntax, a subject/verb inversion being necessary to understand the meaning (I am me).

Replacing "me" by "as for me" in this context will not do. "As for me" is fine in writing after an enumeration that can consist of just one element.

There are various ways to formulate this type of opposition.

1/ • Personally, I like pizza.

2/  • What's making me unconfortable is the cold. (possibly stressed "me")
      • What I can hardly bear is the cold. (possibly stressed "I")
      • Being cold is my problem. (stressed "cold")
      • The cold is my problem. (stressed "cold")