Abstract: Dark matter particles gravitationally trapped inside the Sun may annihilate into Standard Model particles, producing a flux of neutrinos. The prospects of detecting these neutrinos in future multi-kt neutrino detectors designed for other physics searches are explored here. We study the capabilities of a 34/100 kt liquid argon detector and a 100 kt magnetized iron calorimeter detector. These detectors are expected to determine the energy and the direction of the incoming neutrino with unprecedented precision allowing for tests of the dark matter nature at very low dark matter masses, in the range of 10-25 GeV. By suppressing the atmospheric background with angular cuts, these techniques would be sensitive to dark matter-nucleon spin-dependent cross sections at the fb level, reaching down to a few ab for the most favorable annihilation channels and detector technology.