Yes, I've done this many times. Keep them over winter as usual, then in spring start them into growth. When you can see where the new shoots are you can cut/divide them with a sharp knife, making sure there is a shoot(s) on each piece. Dust the cut with some sulphur powder and leave to dry the cut edge overnight. Then pot up as usual.

Many years ago when Alan Titchmarsh presented Gardeners' World he demonstrated how to divide begonias so I've always followed his advice and haven't had any failures yet.