Most dental and medical schools issue the white coat after the bulk of your didactic and pre-clinical work is done. The ceremony recognizes that you are now ready to treat "real" patients in the clinic. Some schools, particularly medical schools have begun to incorporate patient encounters from the very beginning. A number of these schools issue the white coat at the induction ceremony.
I attended FAU med school's inaugural white coat ceremony 3 weeks ago for first years. At my school, our dental and medical white coat ceremonies are this Saturday - both for incoming 3rd years.
IMHO, giving a white coat to an incoming med student is like giving a hammer to a kid long before teaching him the proper way to drive a nail.