You can move them at either time or when they are dormant - June/July. I've had success with all three times and have been given snowdrops freshly dug when in flower or faded. They don't seem to be fussy as long as you re-plant right away and water them in. Cooler weather while in active growth is a plus for transplanting.

I have read that they move best "in the green". That's when I moved mine and they didn't seem to notice that they had been moved!:-)

John Grimshaw , co-author of the book Snowdrops, gave a program on Snowdrops at Winterthur on Sunday. He recommends moving snowdrops while dormant.
Most bulbs produce chlorophyll for a short time , then store the food for later use. Digging and moving is disruptive and can compromise the bulb. Although it can be done in the green, the results are better when the bulbs are dormant and won't have to undergo uprooting and stress.

Don't want to disagree with John Grimshaw, but I have been moving snowdrops for 30 years in the "green" and have never had a problem.

Ditto on moving them anytime. They're tough.