Tire-snow interaction, complicated but essential to better understand the terrain's impact on vehicle performance and design, consists of many nonlinear components coupled in the kinematic and dynamic aspects of vehicles. In this paper, a new methodology is introduced to establish a tire-snow interaction model that allows the study of tire-snow interaction (i.e., the drawbar pull and torque) to the inputs (i.e., the vertical load acting at the tire center and the longitudinal slip) in both time- and frequency-domains. The time-domain analysis enables a description of the model outputs by feeding time-varying inputs obtained from field tests into an explicit, physically-based quasi-static tire-snow model. Comparison of the model outputs to the data recorded in field in situ shows a good agreement in capturing major transient characteristics of the tire-snow interaction. On the other hand, in the frequency domain we also correlate the spectral density functions of individual inputs and outputs to establish an implicit, transfer function-based model, which enables a comparison of the spectra of the input-output relations for the model-based and measured data. The agreement in spectra of the input-output relations suggests the effectiveness of our methodology in better revealing system information about tire-snow interaction.