It's complicated. Hidden Power is determined by the pokemon's DV's and whether or not it stems from Attack or Special Attack depends on it's type. If Hidden Power is a Special type (Psychic, Dark, Grass, Fire, Water, Ice, Dragon, Electric), then it uses Special Attack; if it is Physical type (Normal, Flying, Ghost, Fighting, Steel, Rock, Ground, Bug, Poison), Then it uses Attack.
As far as Countering it goes, Counter ignores it's type and treats it as Normal (so a Ground type can Counter an Ice Hidden Power).
Shorter answer: the move itself is treated as normal (thus physical), but attack or sp. attack is used for damage according to hidden power's attack type (so HP psychic would still be a special attack, for example).