Learn German: Zuerst spürt er sie.

Because both are pronouns. In the German middle field (the part of the sentence after the conjugated verb), a subject pronoun always comes before an object pronoun. If the subject were a noun instead of er, the object pronoun sie would usually jump in front of it, like in Zuerst spürt sie der Mann.

The translation says he senses 'it', but the German word is sie. What does sie refer to here?

It refers to a grammatically feminine noun that was mentioned previously. In German, pronouns must match the gender of the noun they replace. If he were sensing the danger (die Gefahr) or the cold (die Kälte), it becomes sie, which translates to 'it' in English rather than 'she'.

Could we use fühlt instead of spürt here?

Yes, but there is a slight nuance. Fühlen is the general word for feeling (emotions or physical touch), while spüren often implies a more subtle sensing or detecting of something, like a presence, a change in temperature, or an unseen danger.