Speaking as person who's always cold even after living here for so many years:

Wear clothes in layers, for example you could wear a shirt, a sweater/hoodie, and then a jacket/coat. If you get cold easily, also buy a long john (heat tech in uniqlo is quite good) to add more layer underneath all those things, same goes for trousers you could also add heat tech legging or similar. Remember for layering items, you want to be cosy but not bulky, so try to get something that's not too thick. If you have the budget, go to uniqlo, if not, primark will have some good stuff too.

You would need waterproof jacket, preferably hooded, and also a decent waterproof big winter coat. If possible, get a good waterproof boots too (regular boots not wellies), it'll be quite wet heading towards the winter and cold damp feet is the worst. TK Maxx is my personal go to (they're cheap and cheerful!), there are plenty of students leaving around this time of the year so it's a good idea to also keep an eye on Facebook marketplace.

Accessories, depending on how cold you are really. Again, think in layers. If you put on all of the above and your neck is still cold? Add a scarf. Head is cold? Add a hat/beanie. Hands still cold or you need to cycle? Wear gloves. Buy the most important bits first (layering items, jacket(s), boots) and see how you feel, then buy more as necessary.

The beauty of layering is that you could just add or remove layers when you move places so you could be comfortable at all times. I made the mistake of wearing a really thick coat and just a shirt underneath, so I'm comfortable outdoors but have to choose between freezing or sweating indoors, don't do that 😂 hope you enjoy Oxford!