A cotton coat feels like cotton to me. My dog Winston is a cotton coat, but he is pin straight so I don't think curly vs. straight makes the distinction between cotton or silk. However, in the yorkshire terrier, a true silky coat will be pin straight, but a modified silky coat can be curly. Here is a pic of my Winston who has a cotton coat, you can sort of see the texture is thicker. He mats like crazy and it's tough to keep the coat longish without a lot of work. He also cannot get away with a cheaper or inferior conditioner, and I need to buy the good stuff for him.
Don't worry, Wallee's hair will grow back!
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