。
She gave me a cold look.
Literal
She [topic-は] me [object-を] cold eyes [with-で] looked-at.
冷たい目で見る is the stock phrase for looking at someone coldly or contemptuously — 冷たい ('cold') applied metaphorically to the eyes. で here marks the manner of looking, the same で seen in 笑顔で ('with a smile'), 真剣な目で ('with a serious gaze'). The construction puts emotional content in the modifier of 目, not in the verb 見る itself — letting Japanese build a wide range of charged looks (優しい目で 'tenderly,' 厳しい目で 'sternly,' 疑いの目で 'suspiciously') from the same template.