The spell Polar Midnight is a spell with the cold descriptor which also deals dexterity damage. Does Cold Resistance reduce the amount of dexterity damage taken from the spell?
Short answer: it does not.
As you can see in the sources below, Energy Resistance stops just the damage from the specified energy type, and the text of the spell Resist Energy further clarifies that it does not prevents any other effect from happening.
Let's examine some of the sources of energy resistance:
A creature with resistance to energy has the ability (usually extraordinary) to ignore some damage of a certain type per attack, but it does not have total immunity.
Each resistance ability is defined by what energy type it resists and how many points of damage are resisted. It doesn't matter whether the damage has a mundane or magical source.
When resistance completely negates the damage from an energy attack, the attack does not disrupt a spell. This resistance does not stack with the resistance that a spell might provide.
A suit of armor or a shield with this special ability protects against one type of energy (acid, cold, electricity, fire, or sonic) and is designed with patterns depicting the element it protects against. The armor absorbs the first 10 points of energy damage per attack that the wearer would normally take (similar to the resist energy spell).
Resist Energy: This abjuration grants a creature limited protection from damage of whichever one of five energy types you select: acid, cold, electricity, fire, or sonic. The subject gains resist energy 10 against the energy type chosen, meaning that each time the creature is subjected to such damage (whether from a natural or magical source), that damage is reduced by 10 points before being applied to the creature's hit points. The value of the energy resistance granted increases to 20 points at 7th level and to a maximum of 30 points at 11th level. The spell protects the recipient's equipment as well.
Resist energy absorbs only damage. The subject could still suffer unfortunate side effects.
Protection from Energy: Protection from energy grants temporary immunity to the type of energy you specify when you cast it (acid, cold, electricity, fire, or sonic). When the spell absorbs 12 points per caster level of energy damage (to a maximum of 120 points at 10th level), it is discharged.