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The pre-merger (early-warning) gravitational-wave (GW) detection and localization of a compact binary merger would enable astronomers to capture potential electromagnetic (EM) emissions around the time of the merger, thus shedding light on the complex physics of the merger. While early detection and sky localization are of primary importance to the multimessenger follow-up of the event, improved estimates of luminosity distance and orbital inclination could also provide insights on the observability of the EM emission. In this work, we demonstrate that the inclusion of higher modes of gravitational radiation, which vibrate at higher multiples of the orbital frequency than the dominant mode, would significantly improve the earlywarning estimates of the luminosity distance and orbital inclination of the binary. This will help astronomers to better determine their follow-up strategy. Focusing on future observing runs of the ground-based GW detector network [O5 run of LIGOVirgo-KAGRA, Voyager, and third-generation (3G) detectors], we show that for a range of masses spanning the neutron-star black-hole binaries that are potentially EM-bright, the inclusion of higher modes improve the luminosity distance estimates by a factor of ~ 1 - 1.5 (1.1 - 2) [1.1 - 5] for the O5 (Voyager) [3G] observing scenario, 45 (45) [300] seconds before the merger for the sources located at 100 Mpc. There are significant improvements in orbital inclination estimates as well. We also investigate these improvements with varying sky-location and polarization angle. Combining the luminosity distance uncertainties with localization skyarea estimates, we find that the number of galaxies within localization volume is reduced by a factor of ~ 1 - 2.5 (1.2 - 4) [1.2 - 10] with the inclusion of higher modes at early-warning time of 45 (45) [300] seconds in O5 (Voyager) [3G].