I find snowdrop stigmas are not very receptive to start with. When the flowers 'drop' from the spathes and it becomes possible to pop open the outers petals to get at the stigma, pollen will not adhere to the stigma tip very easily. But two or three days later much more pollen with stick much more easily. I find it best to pollinate as soon as I can open the flower with my fingers, dusting the stigma whether much pollen seems to be sticking or not. Then go back a couple of days later and try again, when you'll generally find more pollen sticks.
If you're trying to do a deliberate cross, Rob, I wouldn't wait for a flower to open naturally, as in dull or cold weather it might not open for days but the stigma might be receptive inside the closed flower. Pop it open and pollinate as soon as the outers can easily be pressed open.
Snowdrops tend not to be very self-fertile, so provided you get to the stigma with your pollen before the bees, you stand a good chance of not having your cross spoiled. However, some snowdrops produce a lot of pollen, and if this falls it will stick to the stigma, and even if it won't pollinate, it can still stop your pollen from adhering and pollinating.