Learn Spanish (Latin America): Aquí tengo mucho frío.

In English we say "I am cold", but in Spanish, basic physical states like cold, heat, hunger, and thirst are treated as things you possess. Because of this, you use the verb tener (to have). You are literally saying "I have cold."

Why is it mucho frío instead of muy frío? Doesn't muy mean "very"?

Yes, muy means "very", but because you are using the verb tener (to have), frío is acting as a noun here (meaning "coldness"). In Spanish, you use mucho (much or a lot of) to describe amounts of a noun. You are literally saying "I have a lot of cold."

Is the word yo (I) missing before tengo?

It is omitted, which is the standard way to speak in Spanish. Because the verb form tengo only ever means "I have", adding yo isn't necessary to understand who is being talked about.

Can I change the word order and say Tengo mucho frío aquí?

Yes, absolutely! Placing aquí (here) at the beginning of the sentence just adds a little extra focus to the location, similar to saying "Here, I am very cold" in English.