Yes, very interesting question! I think it is fondamentally geniticaly determined... But I wonder if some environmental factors affects survival of some plants (ex : maybe white plants need more Mg to grow well?). And maybe some living factors like specific insects for pollination further some colors in some regions
There are a lot of white cyps where we live now. The more common are light pink. Dark flowers are very rare. We find C. acaule mainly where there are a lot of firs and spruces. Soil is an acidic loam ... Podzol. I think that there is a lot of Mg since serpentine is common here (asbestos... you know...). Although there are spruce-fir stands, we live in an ecological region called "Erabliere à bouleau jaune de l'Est" (a sugar maple bioclimatic domain).
I saw a lot of dark pink flowers in stands from the Canadian Shield in fir-spruce stands with sandy soil. The ecological domain was a more « northern » one (fir). The plants were growing in acidic soil in coniferous forest growing in that area (OK... acidic is not an accurate measure... sorry).
For the light, I don't think it influences coloration since we can find white, light pink and dark pink flowers in shade, dappled shade and sometimes full sun. Actually Cypripedium acaule seems to grow better with a lot of light in our province but I guess that like many plants it needs more shade in warmer areas.