. What is a good place to go to get affordable winter clothing that will last?
A clothes shop. There are plenty of malls in Warsaw. You can get anything you need.
Prices are rather higher in Europe than in the US (as is quality and style), so you may save money buying there. You'd have to decide whether the space winter clothing would take in luggage or the cost of excess baggage or shipping would make the small saving worth the effort. There are good value shops here. Also markets which can be very cheap.
You should remember that although the outside can be cold (-10 in Warsaw very often, warmer in a mild winter, colder in a bad one), buildings are heated to the point of stuffiness inside. I usually favour a good heavy coat and light-ish clothing underneath. (But perhaps not as light as you're used to) You might want long johns or a thermal vest (a vest in the English sense of the word, not the AmEng meaning) for those few days when the temperature falls below -10 or so. A hat that covers the ears is a good idea for the worst days. Most people here wear them.
I tried to edit the post but left it too late to press send.
Please take seriously what I said about thermal underwear - it allows you to dress warmly but not look like the Michelin Man. @Warszawski mentioned that it can go down to -25c on a few days. This is fortunately very rare but can happen and is the tmperature is unpredictable. Thermals will give you an extra layer for those days. Aa hat that covers the ears is good for when it goes below about -5c (lasts at least a month) and gloves. People will stare at you if you don't have them. You should buy those here. Good dry boots are a must, but are heavy, so buy them here. Things like sweaters are cheap, and Marks & Spencer (their range is usually shown on their website) is a good place to shop. The big supermarkets like Carrefour are extremely cheap, and if you are a student you should get a discount at some chain stores.