"White" is more than a bit of a loaded term, and not really applicable to the time frame you're talking. Be a little more specific w/r/t genetics and you'll likely get better answers.

This is probably a better question to ask to /r/askanthropology. They'll be very familiar with the samples collected throughout Europe. They've been able to extract DNA from these samples and searched for certain tell-tale skin-lightening genes, SLC24A5 and SLC45A2. The presence of those will indicate that skin lightening as compared with the people who immigrated to Europe from Africa and Asia, has been happening.

But the term "white" is a highly loaded term and has no scientific validity as a defined sub-set of people.

Obvious from off the top of my head, the Sami.