I had difficulty finding an OAT date back in August, so I called border services to get a verbal confirmation if I would be allowed to cross the border into the US to write one. He asked if I was in medical school right now, I mentioned "no, I am writing a test to get into one". He declared it as non-essential at that time. I was thankfully able to find a seat in Ottawa and drove 4 hours to write it.
My recommendation would be, to find a seat in Canada, avoid last-minute hassle at the border; because apparently it's up to the US border officer on duty on who gets to go through ( this is all pertaining to my own experience from Aug. * please call respective border crossing office * please note situation could have changed)