If you have no winter experience but are happy to walk in any weather any other time of year and your nav is on the ball. I would say the best thing to do is go on a winter skills course winter walking is a different game.
You need crampons and a walking axe, if you slip on snow/ice with out a axe you would find it hard to stop yourself. That’s why it’s a good idea to do a winter skills course as they will teach you how to use all the gear.
Crampon wise if your boots are in class B1 then you can use crampons that are C1 but not any higher. The boot is the part of the system which provides the stiffness for the crampon. Grivel G10’s are a very good walking crampon.
Have a word with your local gear shop for advice, they might also run winter courses. Tiso have some good staff and also run courses.