Glacitectonically thrusted blocks of unlithified sediment are commonly inferred to have been frozen during thrusting, with implications for paleoclimate and glacier dynamics. We inferred strain patterns within thrusted blocks of glaciolacustrine mud in the Rubjerg Knude and Møns Klint glacitectonic complexes of coastal Denmark to try to assess whether the mud was frozen during thrusting. Fabrics based on the anisotropy of magnetic susceptibility (AMS) of the muds are interpreted with results of ring-shear experiments and models of AMS fabric development during layer-parallel shortening (LPS). In intact distal stratigraphy, fabrics indicate moderate LPS. Fabrics where thrusts have disrupted more proximal stratigraphy indicate rotation of mud sheets during thrusting with insufficient penetrative strain to reset the LPS fabric. The exception is within decimeters of faults at Rubjerg Knude where shear overprinted the LPS fabric. Although these data indicate that mud sheets were mostly rigid during thrusting, this is not necessarily evidence of permafrost. Critical-taper theory indicates that even a gentle slope of the proglacial surface away from the glacier margin would have allowed slip without internal deformation of thrust sheets, requiring only minimal pore-water pressures.