Can I use cellular data to receive in-flight weather on my iPad?
Can you? Yes, but service might be slow or spotty.

May you do so legally? That probably depends. The FAA doesn't specifically prohibit the use of any electronics in GA aircraft; they only state that under 14 CFR §91.21, those aboard an IFR aircraft can't operate electronic devices unless they are


  
  Portable voice recorders;
  Hearing aids;
  Heart pacemakers;
  Electric shavers; or
  Any other portable electronic device that the operator of the aircraft has determined will not cause interference with the navigation or communication system of the aircraft on which it is to be used. [emphasis mine]
  


It's possibly questionable that you as the pilot are an authority on whether or not your devices will cause interference.

The FCC, however, has banned the use of cellular phones in flight per 47 CFR §22.925: 


  Cellular telephones installed in or carried aboard airplanes, balloons or any other type of aircraft must not be operated while such aircraft are airborne (not touching the ground). When any aircraft leaves the ground, all cellular telephones on board that aircraft must be turned off. 


Whether or not that can be interpreted to apply to an iPad's 3G connection is pretty iffy.