Learn Italian: Gennaio e febbraio sono mesi molto freddi. - January and February are very cold months.

In Italian, the months of the year and days of the week are not capitalized unless they appear at the very beginning of a sentence. That is why Gennaio has a capital letter here, but febbraio does not!

Is the word for month (mesi) masculine or feminine?

It is masculine! The singular word is il mese (the month). Because it is a masculine noun that ends in -e in the singular, the plural form changes that -e to an -i, making it i mesi.

Since everything else is plural, why doesn't molto change to molti?

When molto is used to mean "very" and comes before an adjective (like freddi), it acts as an adverb and never changes its ending. It only changes endings (becoming molti, molta, etc.) when it means "many" or "a lot of" and is attached to a noun.

Why does freddi end in -i here?

Adjectives in Italian must match the noun they describe in gender and number. Since they are describing mesi (a masculine plural noun), the base adjective freddo (cold) must change its ending to the masculine plural -i, becoming freddi.