The motion of a slender body in fluid beneath an ice cover coated with wet snow is considered. It is assumed that the fluid is ideal and incompressible, and the fluid flow is potential. The ice cover is modeled by a viscoelastic floating plate, the snow cover is modeled by a viscous layer. Formulas for calculating the wave resistance, the lift force, and the trimming moment exerted on a slender body which moves unsteadily and rectilinearly in fluid beneath the ice and snow covers are analytically obtained. A numerical analysis of the results shows that the snow cover reduces the absolute values of the extrema of hydrodynamic loads. The combined influence of increase in the snow-cover thickness, decrease in the depth of body's submergence, increase in the ice-cover thickness, and decrease in the depth of water basin on the magnitude of hydrodynamic loads is analyzed.