I didn't think a shed hunter ever stopped looking.
I start watching for sheds the last part of December while bowhunting. If I am in a good area for any reason from Jan till the middle of March, I will walk around the area. I also do alot of scouting to keep track of where the deer are feeding and if the bucks are still carrying. From the middle of March till green up, every free moment my son and I have are spent tromping around the countryside looking for sheds.
Last year we found 70 whitetail sheds and a moose shed. Here's a picture of most of them.