I would hope that the reactor cooling systen in a nuclear power plant would be designed to survive an EMP event.
Pumps can be driven by diesel engines, which can be started by compresed air, or by hand in small sizes.
Basic electrical equipment can be hardened/protected against EMP, the military do this, and I would hope that this is true of nuclear power plants also.
I would still prefer not to live downwind of one though !