It has been my understanding that the best time to move / divide snowdrops is when they are in bloom or shortly afterwards. Checking a few websites a moment ago, I see at least one that recommends waiting until they are dormant. So - take your pick. It would be pretty hard in my opinion to kill them one way or the other. Personally, I think dividing and moving snowdrops while the leaves are still green is more practical because you can so easily see what you are dealing with.
If you can dig and move snowdrops - bravo! And I have NEVER had a swathe of snowdrops as one might see in the British magazines Back to this coast, i have not had success moving special patches that were about to be paved over etc (the usual reasons for moving plants perhaps?) Yet they will emerge from a muddy path that contractors stomped over repeatedly the previous summer! I would especially like to grow some snowdrops in pots — Do you have any tried true methods @Margot
I have never been a huge fan of snowdrops - much less a collector. They have so much going for them but, except for the ubiquitous, self-seeding daffodils, I grow only the bulbs native to this former Garry Oak meadow. Truth be told, snowdrops, crocuses, daffodils, tulips, etc. tend to outshine the modest native bulbs and that is something I won't allow! Having said that, common snowdrops appear here and there in my garden, sometimes showing up in unexpected, rather inhospitable places. I sometimes try to relegate them to pots where they do fairly well and multiply. It is baffling to me (and obviously to you too, Georgia), why you have found them to be so ungrateful. I have no ideas except that maybe they thrive on neglect.
There's a chap by the name of Rod Begbie who maintains a website on all things Galanthus. This is what he says about dividing/splitting....