$349 million in Canadian dairy exports last year is a fair chunk of change.
http://aimis-simia-cdic-ccil.agr.gc.ca/rp/index-eng.cfm?action=rR&pdctc=&r=139
It's less than we import, and it could be greater, but it could be greater working within our current system if there was the will do o that. Maybe American dairy subsidies are down, but does that include all the subsidies for corn producers and other producers whos products go into dairy?
New Zealand is always brought up as a success story, but their domestic prices increased when supply management ended.  They aren't a small market on the doorstep of a large market and producer.  They're a small market on an island no one else is too interested in selling to.