Why do you need a rug in your closet? It’s a small space. Nothing else needed

To make it look a bit more luxurious. Also even with new insulation in my home in the cold New York winters the floor can be cold in the morning when walking in barefoot and getting dressed LOL

I personally wouldn’t worry about luxury in a closet. I have wall to wall carpet in my master (previous owner selection) and it’s a pain to keep clean. I’d much rather swiffer hardwood floors!! If you need something to keep your feet warm, choose a small area rug you like that fits the space.