We investigate data from the Galactic Effelsberg–Bonn H i Survey ( EBHIS ) , supplemented with data from the third release of the Galactic All Sky Survey ( GASS III ) observed at Parkes . We explore the all sky distribution of the local Galactic H i gas with |v _ { LSR } | < 25 km s ^ { -1 } on angular scales of 11′ to 16′ . Unsharp masking ( USM ) is applied to extract small scale features . We find cold filaments that are aligned with polarized dust emission and conclude that the cold neutral medium ( CNM ) is mostly organized in sheets that are , because of projection effects , observed as filaments . These filaments are associated with dust ridges , aligned with the magnetic field measured on the structures by Planck at 353 GHz . The CNM above latitudes |b| > 20 ^ { \circ } is described by a log-normal distribution , with a median Doppler temperature T _ { D } = 223 K , derived from observed line widths that include turbulent contributions . The median neutral hydrogen ( HI ) column density is N _ { HI } \simeq 10 ^ { 19.1 } { cm ^ { -2 } } . These CNM structures are embedded within a warm neutral medium ( WNM ) with N _ { HI } \simeq 10 ^ { 20 } { cm ^ { -2 } } . Assuming an average distance of 100 pc , we derive for the CNM sheets a thickness of \lesssim 0.3 pc . Adopting a magnetic field strength of B _ { tot } = ( 6.0 \pm 1.8 ) \mu G , proposed by Heiles & Troland 2005 , and assuming that the CNM filaments are confined by magnetic pressure , we estimate a thickness of 0.09 pc . Correspondingly the median volume density is in the range 14 \lesssim n \lesssim 47 { cm ^ { -3 } } .