Podiatry is a medical profession.
Why would it be any different?
That being said: Have seen people date in my class rampantly. Some date classmates, some prefer (and for good reason) to date outside of the class or medical field completely. Some have long distance relationships continuing. Some are married. Some met their spouses during residency. Some are still single after residency.
Really depends what you want. I locked it down before starting school. Sure its nice to flex your white coat pics and get dates in a different city, but its also nice being married and having something consistent and stable when you're being doused by the fire hose that is school. My relationships affect how I do in class. If my relationship is rock solid going in, I can focus on school without having to worry about break ups, depression, insecurities, all the drama and emotional drain associated with dating.
It is completely doable and you will have time. But you need to understand people outside of this realm do not realize how much time you need to commit to school.