Dogs, cats and rabbits understand the concept of a blanket and usually like to get covered by it when it’s too cold. So I think it’s not far fetched to assume they understand clothes.
My smallest dog is probably the smartest, and he not only understands "covering means warmth" but he also has a favorite throw blanket. Even when they've been freshly washed he prefers the flour tortilla patterned blanket, as it's the warmest.
And when it gets warmer overnight, he will switch to a cooler blanket.
Haven't managed to train him to put his unused blankets away, he just leaves them wherever he dragged it to last.