Stellar winds from neutron stars It seems that this question has not really been explored in the literature. Do isolated neutron stars (which do not accrete material) emit stellar wind? If yes, what composition would it have? If yes, what will be the rate of mass loss for the star?
One might also think up that the process of Hawking radiation might possibly be applicable to neutron stars, where negative energy particles get trapped in the nuclear star atmosphere (instead of crossing the horizon in case of black holes), which would also lead to some sort of evaporation and corresponding wind. However, in this question I am more interested in 'classical' winds.
 A: I don't claim to be an expert on this topic, but I found this recent review paper: arXiv:1211.0852. Here's a short summary covering the questions above.
Isolated neutron stars can emit a wind powered by the rotational energy of the star. As it slows, it loses energy at a rate $\dot{E} = 4\pi^2I\dot{P}/P^3$ where $E$ is the rotational kinetic energy of the star, $P$ is its rotational period, $I$ is its moment of inertia and a dot denotes a time derivative. This energy loss can drive a relativistic wind of electrons and positrons, which is visible via synchrotron radiation from the interaction of the wind particles with the (often very strong!) local magnetic field. Whether all neutron stars DO emit a wind is as yet unknown.
87 out of 103 galactic objects (at least tentatively) identified as neutron stars have an associated detection showing or suggesting a wind. These are primarily stars not in binary systems, but instead discovered in supernova remnants.
As to Hawking radiation, my understanding is that the process requires an event horizon to occur, but maybe someone with a better understanding of that process can weight in.
A: Young neutron stars and the winds they energize, lay cause to some of the most extreme
physical environments in the universe. The exact plasma and wind production
mechanism are not well understood, but the basic picture is as follows.
At the stellar surface, the pulsar’s huge magnetic fields and rapid rotation induce
enormous electric fields within the magnetosphere, these consequently tear particles
from the stellar surface and accelerate them to high energies. Plasma then fills
the magnetosphere and the extreme magnetic field present is sufficient to cause
the plasma to rigidly co-rotate. However, this co-rotation must cease somewhere
near the light cylinder, and the particles flow along the opened magnetic field lines,
carrying away energy in the form of an ultrarelativistic magnetized wind.
In those cases, where the conditions are conducive to the formation of a rapidly rotating
neutron star, a pulsar wind, driven by the pulsar spin-down power is likely to always be formed. 

If yes, what composition would it have? If yes, what will be the rate of mass loss for the star?

The first of the above questions depends on the angle that the axis of the stars magnetic field makes with its rotational axis. In reality, pulsars will almost always be oblique rotators (with $\mathbf{B}$ miss-aligned to the axis of rotation). In this case the wind from the star will take the form of a striped wind. However, most mathematical models of pulsars assume and aligned rotator and instead of modelling this stripped wind explicitly they do this implicitly - this avoids 3D models and a massive increase in complexity. 
The rate of mass loss due to such a wind is something that we do not know for sure. However, it is likely to be directly ascociated with the spin-down power of the star - but again, depending on the 'obliqeness' of the rotation, this will vary.

One might also think up that the process of Hawking radiation might possibly be applicable to neutron stars...

I know of no reason to suggest that Hawking Radiation would act in the way you have suggested. This mechanism is purely associated with event horizons. However, one mechanism associated predominantly with black-holes and that may have some bearing for pulsars is the Blandford–Znajek process. This is a mechanism for the extraction of energy from a rotating black hole. It is one of the best explanations for the way quasars are powered. It requires an accretion disc with a strong polar magnetic field around a spinning black hole. The magnetic field extracts spin energy and the power can be estimated as the energy density at the speed of light cylinder. I have never seen suggestion of this process being applicable to neutron stars, but I have not looked - to me it would be a far more likely mechanism...
I hope this helps.
