Context. White dwarfs are the fossils left by the evolution of low- and intermediate-mass stars, and have very long evolutionary timescales. This allows us to use them to explore the properties of old populations, like the Galactic halo.; Aims. We present a population synthesis study of the luminosity function of halo white dwarfs, aimed at investigating which information can be derived from the currently available observed data.; Methods. We employ an up-to-date population synthesis code based on Monte Carlo techniques, which incorporates the most recent and reliable cooling sequences for metal-poor progenitors as well as an accurate modeling of the observational biases.; Results. We find that because the observed sample of halo white dwarfs is restricted to the brightest stars, only the hot branch of the white dwarf luminosity function can be used for these purposes, and that its shape function is almost insensitive to the most relevant inputs, such as the adopted cooling sequences, the initial mass function, the density profile of the stellar spheroid, or the adopted fraction of unresolved binaries. Moreover, since the cutoff of the observed luminosity has not yet been determined only the lower limits to the age of the halo population can be placed.; Conclusions. We conclude that the current observed sample of the halo white dwarf population is still too small to obtain definite conclusions about the properties of the stellar halo, and the recently computed white dwarf cooling sequences, which incorporate residual hydrogen burning, should be assessed using metal-poor globular clusters