Mass of particles in GR field

In QM energy is related to frequency by h_bar. In Relativity mass is
related to energy. A particle at rest can be represented by a wave
function exp(-i*w_0*t) where w_0 is the frequency corresponding to the
rest mass of the particle. GR predicts a gravitational red shift. I
assume that this red shift applies to this rest mass frequency as
well. Therefore, if I'm thinking about this correctly, the rest mass
of a particle deep in a gravitational well (wrt the observer) is
reduced. Is this correct, or am I missing a key concept?

If this is correct, then by the time such a particle reaches the event
horizon it's apparent mass (as seen by the observer higher in the
well) will be reduced to zero (since g_00 goes to zero at that
point). If the particle was allowed to fall freely to this point, I
assume all the rest mass energy has been converted to kinetic energy.
Of course in the frame comoving with the particle it would always have
the original rest mass.

I'm also not quite sure what it means to the observer that the rest
mass of the particle has been reduced. How would he measure this,
since by definition he can't be with the particle. Would this be
observable, or is this "mass reduction" meaningless in terms of
observations?

.

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