Like NDY says, it depends. For a real answer someone would really need to have a daily monitoring record. I haven't heard yet of anyone that does, but its certainly possible.
We have a place just east of Eastern Lake a couple of hundred yards. We rent it out and normally only get there four or five times a year in the off season. In the 10 years we've owned it, I only remember EL actually breaking out while we were there twice. Some of those times we visited it has been open for a while and it had an inflow at high tide and an outflow at low tide, most of those times it's been closed off completely. We consider being there when they break open especially lucky times as its been so rare for us and we like it.
When it breaks through, whether you get colored water in front of you depends on the nearshore current at the time. Some times it flows west to east, some times east to west. I think the prevailing current is east to west, but we've been there when it was open and either only the area right in front of the outlet was brown or it was flowing east from us.
I wonder about lake openings and closings mainly because I'm curious. If I were more curious I'd start a web site or maybe a topic on Sowal forums and solicit folks to send sightings of openings and dates so I could track it.
If you run across anyone that can give you more specific information, please post as I'd be interested in hearing about it.