In the first part of this thesis we describe the functioning principle of the scanning hall probe microscope (SHPM), and we present a summary of the theoretical and experimental knowledge on the dipolar-coupled Ising ferromagnet LiHoF4. In the second chapter we present the experimental setup that allows us to perform SHPM imaging at ultra low temperatures. The main components; microscope head, dilution refrigerator (DR), and vibration-free cryostat, are described in detail. We also explain the choice of samples geometries used, and the surface preparation performed. Some modifications made to the microscope to enhance its performance are also detailed. The experimental results are separated into two chapters, the first with more qualitative observations, and the second one where we attempt to extract quantitative information from the images. We present different sets of SHPM images taken on different sample geometries, with two sample orientations (a-a and a-c planes), at different temperatures (from 20 mK to 1.6 K), and under transverse magnetic fields up to 3 Tesla. In the first chapter we discuss the ground state domain structure and how the order parameters perturb it. In the second chapter we attempt to extract a detailed domain structure by a rudimentary image treatment. We also describe the change in magnetization with temperature, and compare it with other experimental data.