There's no "snow shoes"* in base game, just skis.
Deeper the snow, more and faster fatigue builds up. And higher encumbrance can really cause the fatigue to skyrocket.
Early mornings often have a hard crust that's able to carry person, once sun goes up, the crust can thaw to thin or even all gone, and won't be able to carry person any longer.
*One could mod the game to have snow shoes, but they'd be as fast as skis, which is unreasonable.