Does wearing running shoes all day long count as a run?

What counts as a run?  Today while doing the tourist thing at the Little Mermaid my foot went straight through the ice and into the Baltic Sea.  At first I thought this is a disaster as the temperature did not go above 0 all day (a case of frost bite, not so good for a months worth of running!)  Then I got a brain wave and spent the rest of the day walking around in running shoes after changing back at the hotel.  On a serious note I did manage a 30 minute run in the early evening.  Once again dark and freezing temperatures and I am looking forward to flying back tomorrow so I can up the distance on more familiar territory.