Was there a domestic ornamental rug making tradition in Medieval Europe? What types of patterns were common and who would have access to them?

Central Asia is famous for its luxurious "Persian" rugs that are in high demand even today with cultures from Afghanistan, to Northern Africa and beyond having ornamental rugs in regular people's homes, often as replacements for furniture.

And I think about Spanish New Mexico who also had a tradition of rug weaving although the blankets are more famous.

I think about Medieval castles filled with rich tapestries and wall hangings, and thresh covered floors and my presumption of thickly laid rugs. In Colonial New Mexico, haciendas in the winter would have inches deep grass/thresh layer which would be covered in blankets, buffalo robes, and rugs that kept the living space warm and the floor soft enough to sleep on.

Would medieval peasant homes have access to locally made rugs for their winter homes? Would the rich and noble have mountains of local rugs to be brought out for winter or would they prefer only imported oriental rugs to show wealth? Was that type of heavy rug layers even common as furniture was common and a floor was just a floor?

I have a Romanian 100% wool traditional rug that was woven about 40 years ago but it lacks the thick, warm, luxuriousness of my Afghan prayer/war rugs. I don't know if that Romanian tradition goes all the way back to the medieval period or is a 19th century "invented tradition" once textiles became cheaper due to industrialization.