Learn Hardcore Italian: Il raffreddore è fastidioso.

Italian normally requires an article with singular countable nouns. To talk about a thing in general (the class as a whole), Italian prefers the definite article: Il raffreddore è fastidioso = colds are annoying (in general). Bare Raffreddore è fastidioso is ungrammatical. Un raffreddore è fastidioso would refer to an individual case (“a cold is annoying”) and sounds odd as a general statement unless you’re contrasting it with something else.

Could I also say I raffreddori sono fastidiosi?

Yes. I raffreddori sono fastidiosi is grammatical and also makes a general statement. Italian often uses the singular with a definite article to generalize, but the plural works too. The singular feels slightly more proverbial/encyclopedic; the plural can sound a bit more concrete.

What gender is raffreddore, and how do I know?

Raffreddore is masculine. A common rule of thumb: many nouns ending in -ore are masculine (e.g., il colore, l’umore, l’errore). Its plural is i raffreddori.

Why is the adjective fastidioso masculine and singular here?