Learn Italian: Fa freddo, chiudo la finestra. - It is cold, I close the window.

In Italian, we use the irregular verb fare (to do / to make) to talk about the weather. So instead of saying "It is cold", Italians literally say "It makes cold" (fa freddo). Fa is the "it" form of this verb.

Where are the words for "it" and "I" in this sentence?

Italian usually drops subject pronouns like io (I) because the verb itself tells you who is doing the action. Fa already means "it makes" or "it does", and the -o ending on chiudo tells us it is the "I" form (I close).

Is chiudo an irregular verb like fare?

No, chiudo comes from the regular verb chiudere (to close). You simply drop the -ere ending and add -o for the "I" form in the present tense.

Would freddo change to fredda to match the feminine word finestra?

No, they belong to separate actions in the sentence. Also, when talking about the weather, freddo acts as a noun (meaning "the cold") rather than a describing word, so it stays exactly as freddo.