We determined the compressive strength of weak layers of faceted crystals and depth hoar using artificially grown samples with a wide range of microstructural morphologies in a cold laboratory setup. Micro-computed tomography (µCT) imaging showed that the microstructures of the artificial samples were comparable to that of natural depth hoar. We performed compression experiments in a displacement controlled testing machine on 92 depth hoar samples with densities ranging from 150 kg m−3 to 350 kg m−3. The compressive strength spanned two orders of magnitude (1–150 kPa) at strain rates of about 10−3 s−1 at $-5^{\circ}\mathrm{C}$ and followed a power law as a function of density. Several microstructural metrics such as the specific surface area, connectivity density and correlation lengths obtained from µCT measurements exhibited a statistically significant relationship with compressive strength. Analysis of the residuals of the power law fit showed that in addition to density, horizontal correlation lengths also correlated with strength. However, in this study, density remained the dominant predictor of the compressive strength of depth hoar.