The real answer is 1938. I've been doing trivia for Michigan Wolverines for awhile now and the correct answer was 1938. It doesn't signify anything. A former Michigan coach (Fielding Yost) came up with the idea of putting a design on the helmets so his passers would be able more easily differentiate their receivers. I don't think it really means anything. I believe they started wearing it during the 20's or 30's because it would make it easier for the players to tell who was on their team. Princeton actuall had the emblem first, and like the previous answer stated, it was used to easily find receivers in downfield. The winged helmet at Michigan was brought in not by Fielding Yost, but by Fritz Crisler in the mid 1930's, who designed the look while coach at Princeton. The pattern is actually a carry-over from the old fashioned thick leather football helmets that were worn before the composite ones that are used now came out. The distinctive design came from where the helmets were stitched together. Several teams carried the design over, like Michigan, Princeton, and Delaware.
University of Texas
Yes. Along with virtually all iterations of the classic "M" logo the University of Michigan football helmet is a federally registered trademark.(note: for a list of protected trademarks for the U of M see related links below)
Michigan with their winged helmet.
It is a warrior helmet and two spears that are crossing each other.
Marshall University has an M on their helmet.
Mississippi state university
It looks like a bull's head