Don't look at me with that icy expression.

Literal

Ice [like-みたいに] cold face do-not [request-くれよ].

冷たい顔 ('cold face/expression') makes the emotional coldness visual and personal. ~しないでくれよ is a casual masculine request not to do something — くれ (casual) + よ (emphasis). ~みたいに is the colloquial version of ~のように ('like').