Yes, it's the right time to move Snowdrops: everyone seems to know that Snowdrops should only be moved “in the green” but many people are not quite sure what that means.
It means that – cruel as it sounds – the best time to move them is right now, early spring, when they are either still flowering, or have just finished: while the stems are still “green”.
The worst time to move (and particularly, the worst time to buy) Snowdrops, is in the middle of summer when all you get is a handful of small, shrivelled, dry brown bulbs, which are almost guaranteed not to grow.
(I'm sure that people who sell dry bulbs only get away with it because they think the purchaser will have forgotten where they bought them, by the time they fail to grow.)
I am not a big fan of people buying snowdrops, particularly from the internet, as they often arrive in a pretty poor state, all dry and limp, having probably been dug up a couple of weeks earlier and left languishing in an office somewhere, before being packed up and posted. Far better is to find someone locally, one of your friends or neighbours, who has a good show of Snowdrops, and ask them if they would be kind enough to give you a clump or two. Most people are happy to share, and just one or two biggish clumps can be enough to get you started.
The trick to digging up Snowdrops is to insert a fork vertically next to the clump, go deeper than you think you need to, then lever up the entire clump in one go. Once it is out of the ground, shake off the excess soil – back into the hole from which they came – and once you can see all the bulbs, grasp the clump gently but firmly, and pull it apart from the bottom. Don't ever try to pull it apart by tugging on the leaves, you will just break them: always work from below.
You will be surprised how many bulbs there are in one congested clump, and usually you will be able to split the clump into five or six decent handfuls. These can then be planted out, not in neat rows, but in a pleasantly random fashion (the photo above is an exception to this, as the Client specifically wanted a row of them under the hedge) and the best situation for Snowdrops is under trees, or naturalized in grass, as long as you are able to put off mowing until the foliage has died right down.
To plant them, dig a hole about the size of your fist, and as deep as you reasonably can: the commonest mistake is to plant them too shallowly, so I always go the full depth of the trowel, even if it does take a bit of time. Look at the stems of the ones you are planting – it is essential that all the pale, whitish part of the stem is underground again. Make sure to shake off all the soil from below the bulbs: you don't want soil under them, you want soil on top of them! I usually line them up in my hand, bulbs down and leaves upwards (don't laugh, I've seen people just thrust a tangled handful into the ground and expect them to sort themselves out) then insert it into the hole, holding the stems together with one hand, while I push the loose soil down into the hole, making sure the bulbs are right at the bottom, and are firmly contacting the soil. Then fill the hole up to the top, and by holding the stems all together, they should be able to stand up by themselves once you have finished.
Leave the stems and flowers, don't cut any of it back after planting, even if they look quite sad and wilted: just water them well, and maybe give them some liquid feed – a balanced feed such as Growmore, or some liquid seaweed fertiliser will be fine. This helps them to settle in and make good fat bulbs ready for flowering next year. Best of all, the ones which have finished flowering will be setting seed, so you are already well on the way to establishing your new colony!