The candidates started 'slinging mud' (at each other) early in the campaign.
His shoes were covered with 'mud'. = His shoes were caked in/with 'mud'.
The scandal ruined his reputation and now 'his name is mud'.
(..) ...and on top of it all ... ...the comanches they went and took the horses, so ... ...he was starving, delirious... ...and crawles up into this mud ... ...like the group of trees out there in the middle of nowhere ... ...just sticking up in this ocean of scrub ... ...and he found religion. (..)2015 The Revenant