If I want to take winter session at another college, should I make admission at that school?

Should I open an account at that college?

Not if you are just going to take one class. You just sign up for the class you want as a non-matriculated student.

Ask the Registrar at that school how to proceed if you are taking a class as a visiting student.

And before you take any class as a visiting student be certain it will be accepted by your home college. Get a sign-off in advance from your academic advisor/Registrar (whoever is responsible for that at your college) in advance and in writing. FWIW my S’s college would not accept classes taken by an enrolled student at a 2 year college for credit so be careful.