We suggest that recent neutrino puzzles that are the solar and atmospheric neutrino deficits as well as the possible neutrino oscillations reported by the LSND experiment and the possibility of massive neutrinos providing the hot component of the cosmological dark matter, can all be naturally explained by assuming existence of a mirror world described by an ``electroweak'' gauge symmetry $[SU(2)\times U(1)]'$, with the breaking scale larger by about factor of 30 than the scale of the standard $SU(2)\times U(1)$ model. An interesting aspect of this model is that the sterile neutrinos arise from the hidden mirror sector of the theory and thus their lightness is more natural than in the usual neutrino mass scenarios. The needed pattern of the neutrino mass matrix in this model is obtained by assuming a conserved ZKM-type global lepton number $\bar L=L_e+L_\mu-L_\tau$, which is violated by Planck scale effects. One implication of our proposal is that bulk of the dark matter in the universe is a warm dark matter consisting of few KeV mass particles rather than the 100 GeV range particles of the currently popular cold dark matter scenarios.