No. The IVs of the Pokemon you get through in-game trades are fixed, which means their nature is fixed too.
Here's what's great though - in Black/White all the IVs are 20, except for one which is maxed out at 31. So you get a pretty good Pokemon.
Here are the Pokemon you can get, with their maxed IVs:
Petilil or Cottonee: 31 SpAtk
Basculin: 31 Atk
Emolga: 31 Def
Rotom: 31 SpDef
Munchlax: 31 HP