The cold wind completely chilled the traveler's body.
Literal
Cold wind [instrumental-で] that traveler [of-の] body [topic-は] completely was-chilled.
冷える is the intransitive 'to become cold' (matched with the transitive 冷やす 'to make cold/chill'). The で here marks the instrumental cause — 'because of the wind.' すっかり ('completely, entirely') is a common intensifier for thoroughness.