My undergrad's med school (to which I am excited to interview at soon) didn't have white coats for their students at all- or if it did, they never wore them to anything.
Some other schools have them for everything. The place I went to grad school at started having a white coat ceremony for the Ph.D students. The only time I wore a lab coat was when working with radiation or thallium, and the coat is supposed to be disposable.