Leh market at winter, specifically near Moti bazar and 2 shops at main market sales a little old stuff. We Indians, are used to seeing this kind of flea market shop nearby street. You can easily get a down feather jacket theirs in 500–800 INR. Buy one with 1 or 2 upper sizes of yours. These works really fine. As you wear it on top of other clothes, hygiene issue gets short out decently. There are few army canteen shops which sell really good items to keep you warm for the chadar trek including socks, gloves, thermals, balaclava, gumboots etc. These are personal use items and are available at good reasonable rates and I would suggest you buy them. These are one of the few shops which are open in winter. Good Luck!!
Happy Travelling!!