Answer
Yes, you should pack sunscreen for Uruguay, even in winter. Everyday experience treats it as a necessity, not merely as a summer beach accessory.
The reason is that comfort at home and outdoors here depends significantly on the sun, wind and humidity. In winter, direct sunlight can help warm homes, but it remains a factor for the skin that people take into account in everyday clothing and skin care.
The practical approach is simple: keep sunscreen on hand all year round and do not associate it with heat alone. This is especially important on days when you spend a lot of time outdoors, near the water or in areas without shade, even if the temperature seems moderate and the season does not feel like beach season. This is part of the usual preparation for leaving home.