WordNet sense 1 (wrapped up or enclosed within a covering):

enwrapped

WordNet sense 2 (covered with or as if with clothes or a wrap or cloak):

cloaked, clothed, draped, mantled

WordNet sense 3 (giving or marked by complete attention to):

absorbed, captive, engrossed, intent

WordNet sense 4 ((often followed by `to') giving care or attention):

attentive