cover - provide with a covering or cause to be covered; "cover her face with a handkerchief"; "cover the child with a blanket"; "cover the grave with flowers"
bedaub
verb
To spread with a greasy, sticky, or dirty substance:
Some of the natives had really climbed the baobab, and now they were seen rising on all sides, winding along the boughs like reptiles, and advancing slowly but surely, all the time plainly enough discernible, not merely to the eye but to the nostrils, by the horrible odors of the rancid grease with which they bedaub their bodies.
As pointed out by Laffut (2006: 23), exactly the same "transitivizing" prefix was found in older stages of English with verbs such as bedaub, besow, bespatter, and is still productive in the formation of adjectives such as bewinged, bewired, etc.
OTHERS: addle 'to earn, gain'; algate 'always, in every way, in any case'; bain 'ready, willing'; baiter 'to dance'; bask 'bitter, irritating to the senses'; clag 'to bedaub, clog'; hag 'to cut, hew, chop'; nait 'useful, good at need'; ra 'a sail-yard'; risp 'to rub, to grate together; to rasp or file'; scraw 'a scroll or tag of parchment or leather'; slape 'slippery, smooth; also crafty, cunning, deceitful'; snod 'smooth, sleek; even'; stoop 'a post, pillar'; streak "to stroke; to make level, flat or even; to rub or smear; to spread, lay evenly'; uthe 'harmony'; withgang 'success, advantage, profit';
bedaub - spread or daub (a surface)