I don’t know if I would consider pre-Flashpoint Solomon Grundy a straight up zombie. When Cyrus Gold died and was brought back by Slaughter Swamp and the Parlament of Trees to become a new Plant Elemental the process failed and created Solomon Grundy. Each time dies and is reborn on a Monday he regenerated a different aspect of his personality appeared. So he is seen sometimes as a mindless monster, or in Starman an childlike being, or in the latest run of Justice League of America a really smart dude and so on. I’d check out his appearances in Starman for a good story and explanation of who Grundy really is.
Since we only have a panel or two knowledge of the new Earth 2 Grundy this is all speculation. I’m thinking that when Cyrus Gold died he became the champion of the Grey on this Earth. The Grey seems to be comparable to the Rot on the Main DCU Earth (check out recent issues of Animal Man and Swamp Thing). So instead of looking snazzy like Alan did when he became the champion of the Green he looks rotten.
Was he dressed like that when he died? Unless he was a butcher that liked to chop meat with his shirt off, I’d say no. My guess is just like Alan got an outfit when he got his powers, so did Grundy.