Ideally, you want to start in spring/summer for the best chance at success. Make sure that any wintery cold weather is behind you so that your new plants are growing in warmer months with a lot of sunshine. This will speed up growth, help the mother plant recover and will also help to avoid root rot.
If you choose the division method, you can get away with doing it in cooler temperatures as you aren’t growing cuttings and the process is much quicker.