This was driving me insane as well when I first noticed it. Fortunately, this is about the only draw-distance issue that can be easily fixed.
in your Documents/The Witcher 3/user.settings file, locate these two lines in the "[Rendering]" section:
TextureStreamingHeadsDistanceLimit
TextureStreamingCharacterDistanceLimit
I set them to "40000" to match the default "TextureStreamingDistanceLimit" value. Of course, I have no idea what limit these settings have, but safer than sorry.
Save the file (no need to read-only), and launch the game, and no more faces/clothing textures popping in 5 feet from your character.
Screenshot comparison below for proof:
http://screenshotcomparison.com/comparison/130652
This also prevents Geralt's face from turning into a blob every time you load a save. Take note however, that while this fixes texture pop-in on characters, it does not prevent some NPC beards or hair appearing/disappearing at a certain distance (must be a different mesh system controlling this), and thus does nothing for the cutscene pop-in either.
As far as I can tell, upping these settings have zero performance impact and zero side-effects, which makes it seem even more needless to have the NPC textures pop-in so close to your character. Some of the LOD distance limits in this game are baffling.