Yes, in two different ways. Snow piled against a retaining wall adds real weight and pressure behind the wall on top of the soil it's already holding back, and snow sitting on a flat masonry surface like a wall cap, chimney chase cover, or parapet adds direct weight and keeps that surface wet as it slowly melts and refreezes. Both effects are worse on a wall or cap that wasn't detailed to shed water and handle extra load.
Engineers call the extra load snow adds behind a retaining wall a surcharge, and it works on top of whatever pressure the soil itself is already putting on the wall. A wall designed with some margin handles normal snowfall without issue, but snow that's been plowed or shoveled up against a wall is often denser and piled higher than natural snowfall, which can push the total load closer to or past what the wall was originally built to handle, especially on a wall that's already older or marginal.
Flat horizontal surfaces are a separate problem. A wall cap, coping stone, or chimney chase cover collects snow that a vertical wall face would just shed. As that snow melts during the day and refreezes overnight, it concentrates freeze-thaw cycling right at that one surface far more than a vertical face ever sees, and if the joint below isn't properly detailed, meltwater works its way in and speeds up deterioration right at the top of the structure, which is often the hardest part to reach for a repair later.
Chelo's details caps and coping to slope and shed water rather than hold it, sizes drainage behind retaining walls with realistic seasonal loads in mind, and flashes flat surfaces like chase covers so meltwater has somewhere to go instead of sitting and cycling in place year after year.
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