This is stylistic inversion - optional and more formal. Mostly used in formal writing, less so in informal writing or speech, but quite correct.

 https://www.lawlessfrench.com/grammar/inversion-with-nouns/

Bonjour Thanh Tân,

"connected to a belt that the snowshoeing master wears" 

"que porte le maître en raquettes à neige"

I see "that" --> "que" above representing a relative pronoun.

I do not see your proposal as having the same meaning when considering the complete story in context.

Bonne journée

Jim

Inversion is more common in French than English because there are two relative pronouns, qui and que, which tell you whether the preceding noun is subject or object. There is no ambiguity here, but since both words translate to "that" in English, we have to rely on word order more.