Hi Giulia.
Yes that's tricky. I think many people consider date of birth as private and not to share - not because they're sensitive about revealing their age always but it makes them less anonymous. With a name and DOB you can pin down exactly who they are in the public records.

Perhaps ask something else - e.g. retired, working, student to give you an idea. Or try age brackets 0-21, 22-33, 34-43 etc. They are less sensitive for people I think. And if you do ask age questions, ask 2 or 3 other things too. For wording, I suggest you say "We try to only send you informaiton which you will find useful and relevant. By providing this information you will help us do that, thank you".

Hope that's helpful.
Kate