Yes, it is possible.
Here are the locations for where people will tell you the Hidden Power type
For Diamond/Pearl: (EDIT- I made a mistake. The HP guy doesn't exist in diamond/pearl)
For Platinum: Veilstone Game Corner Exchange house
For Heartgold/Soulsilver: Celadon Game Corner
For White/Black: Mistralton City's Pokemon Center
For White2/Black 2: Pokemon World Tournament