if the dark matter of the Universe is constituted by weakly interacting massive particles (WIMP), they would accumulate in the core of astrophysical objects as the Sun and annihilate into particles of the Standard Model. High-energy neutrinos would be produced in the annihilations, both directly and via the subsequent decay of leptons, quarks and bosons. While Cerenkov neutrino detectors/telescopes can only count the number of neutrinos above some threshold energy, we study how, by exploiting their energy resolution, large magnetized iron calorimeter and, possibly, liquid argon and totally active scintillator detectors, planned for future long baseline neutrino experiments, have the capability of reconstructing the neutrino spectrum and might provide information on the dark matter properties. In particular, for a given value of the WIMP mass, we show that a future iron calorimeter could break the degeneracy between the WIMP-proton cross section and the annihilation branching ratios, present for Cerenkov detectors, and constrain their values with good accuracy.