In northern forests, winter is the preferred time for logging operations, since, when wet soils freeze, their strength increases, which ensures a high load-bearing capacity of winter forest roads and reduces the cost of forestry work by increasing the load on forestry equipment, including when driving through frozen lowlands. The present article analyzes frozen loamy–sandy soil, which, at subzero temperatures, behaves like a brittle material with a sufficiently high, but limited, strength. Well-known models commonly use empirical parameters, correlations, and numerical methods to estimate the strength of such materials. An analytical model of the full load–displacement curve would reduce the number of necessary calculations and increase the ability to predict the bearing capacity of winter forest roads. However, there are few of these models. Such models were developed, as a rule, to study stress–strain in concrete and rocks, meaning that researchers have to recalculate the load into stress and displacement into deformation, which is not always simple. This work aimed at theoretically justifying a new analytical model for quantifying the bearing capacity of winter forest roads and assessing the adequacy of the model by comparing it with experimental data. To achieve this purpose, the concepts of fracture mechanics and methods of mathematical modeling were used. The model was verified using experimental data, and model examples for determining the peak load were provided. Prospects for development of the research topic were also considered, taking into account new developments in forest road monitoring for logging management.