Shivering touch is a spell with Cold descriptor. Does it mean, that it should be affected by resistance to cold energy, thus lowering the Dexterity damage dealt by the spell?
No. Energy resistance (from the spell and from magic items that act like the spell) reduces damage "before being applied to the creature’s hit points". (Emphasis added.) Shivering touch doesn't apply damage to a creature's hit points but only to dexterity so cold energy resistance wouldn't affect dexterity damage. Bear in mind that some creatures are immune to ability score drains.
(A whole lot of the book that contains the shivering touch spell is overpowered so is it any surprise this level 3 spell sneaks past cold resistance.)