RC Snubber for synchronous MOSFET (SMPS)
How does the snubber capacitor acts as a short circuit during the
  ringing frequency ? After all it is the one which decides the new
  ringing frequency.


Texas Instruments are somewhat polarizing what happens - it doesn't act as a complete short but it does reduce the ringing frequency AND it also reduces the ringing amplitude. The amplitude reduces because the Q factor of the resonating components is reduced by the snubber resistor.


  Why is Cp (parasitic capacitance) used in the characteristic impedance
  calculation? The equivalent capacitance should have been considered,
  which is Cp + Csnubber.


I'm unsure which document you found this statement - maybe you can point it out?