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We present the design, construction, and performance of a low-temperature scanning Hall probe microscope with submicron lateral resolution and a large scanning range. The detachable microscope head is mounted on the cold flange of a commercial 3He-refrigerator (Oxford Instruments, Heliox VT-50) and operates between room temperature and 300 mK. It is fitted with a three-axis slip-stick nanopositioner that enables precise in situ adjustment of the probe location within a 6×6×7 mm3 space. The local magnetic induction at the sample surface is mapped with an easily changeable microfabricated Hall probe [typically GsAs/AlGaAs or AlGaAs/InGaAs/GaAs Hall sensors with integrated scanning tunnel microscopy (STM) tunneling tips] and can achieve minimum detectable fields 10 mG/ Hz1/2. The Hall probe is brought into very close proximity to the sample surface by sensing and controlling tunnel currents at the integrated STM tip. The instrument is capable of simultaneous tunneling and Hall signal acquisition in surface-tracking mode. We illustrate the potential of the system with images of superconducting vortices at the surface of a Nb thin film down to 372 mK, and also of labyrinth magnetic-domain patterns of an yttrium iron garnet film captured at room temperature.