Yes. I have been growing snowdrops under a flowering cherry, and they are quite happy

No problem, Geradine. There will be no leaves on the tree when the snowdrops flower and they will get full light.

They grow best if you can get some "in the green", ie when they have just finished flowering and still have leaves. Plant bulbs certainly, but if you can get some in late winter either from a garden centre or a friend as well they will normally establish better.