Answer
Yes, it is worth bringing warm clothing, but not heavy clothing for severe frosts. Winter in Uruguay usually does not require a heavy down jacket for northern winters, but humidity, wind, and homes without conventional central heating make layered clothing very useful.
The optimal set includes a windproof jacket, warm clothes for wearing at home, footwear for rainy weather, a blanket, and lightweight layers that can be combined. In summer, temperatures of 30–32 degrees are often easier to tolerate because of the wind and proximity to the ocean, but that does not mean you will be comfortable indoors in winter.
If it is difficult to find shoes, underwear, or outerwear in your size, it makes sense to bring the items you are used to. You can buy the rest after choosing a home and understanding your routine. The main idea is to stay warm at home and avoid overpaying for excess baggage weight.