Is this a butterfly or a moth? Why do you have it at home in winter?

This is a butterfly, which should be a kind of gray butterfly, an ordinary butterfly. See Baidu for details.

The butterfly with gossamer wings is an insect of Lepidoptera Papilionidae. They are all small and medium-sized butterflies (wingspan 1 ~ 3 cm), agile and slender. More than 4500 species have been recorded all over the world. There are 279 known species in China.