Learn Russian: Вчера был сильный ветер, и нам было холодно. - Yesterday there was a strong wind, and we were cold.

In the first half of the sentence, был (was) is masculine to agree with the masculine noun ветер (wind). In the second half, было холодно is an impersonal expression. In impersonal sentences where there is no grammatical subject doing an action, the past tense verb "was" always takes the default neuter form было.

Why is "we" translated as нам instead of мы?

In Russian, you don't say "we were cold." Instead, you use an impersonal structure that literally means "to us it was cold." Because the feeling of coldness is happening to you, you use the Dative case pronoun нам (to us) instead of the Nominative subject pronoun мы (we).

What would it mean if I said мы были холодные by mistake?

If you use the Nominative case and the regular adjective (мы были холодные), it means your physical bodies felt cold to the touch, or that you are emotionally cold people. To express the internal sensation of feeling cold, you must use the Dative case + adverb structure: нам было холодно.

Why does сильный end in -ый?

Сильный (strong) is an adjective describing ветер (wind). Since ветер is the subject of the first clause and is a masculine noun in the Nominative (dictionary) case, the adjective must take the masculine Nominative ending -ый.