Textbooks and course materials
Building on your course syllabus, it will most likely outline the text books and course materials that you will need for the term. These days you can get most of your course materials online, but if your course or professor is old school, you may still need to buy a hard-copy textbook. If possible, try to buy them second hand to save money, but you'll have to do this as soon as possible since the demand for second hand textbooks might exceed the supply.
Week of welcome events
Though there aren't as many week of welcome events in the winter term as there are in the fall term, there are still some fun events you can attend even though most of them may not be in person. Some of these events will have things like free swag so make sure you look them up if you're interested.
Sign up and reconnect with student groups and clubs
If you are a member of student group or club, check in with them at the beginning of the term to see what they have planned for the term. This will help you plan out your involvement with them over the term, and if they have any trips or events planned, there may be limited spots so you might want to sign up before spots fill up.
Start thinking about job prospects
If this is your final term and you haven't started looking up job prospects, now is the time to do it. Some companies may have been recruiting since fall, but some focus their recruitment efforts in winter as well, so make sure to look these up.