Problem:

The new armour patch makes your uniform disappear. You're soldier is just a floating head and when you go to customise her/his armour, it shows 0 for arms, legs, and torso and they can't be clicked on to change.

Solution:

More of a work around than a fix, but in the end, it fixes your problem.

Pick up a mod, from either here or from Nexus, called "Uniform Manager".
Subscribe or install it then load up your game with your broken soldier.
Switch your soldier's loadout from whichever armour is broken to a different one.
In my case, it was the WAR suit; so I switched from the WAR suit to the Warden Armour. After switching, I customised the armour like I wanted it then backed out and clicked the new menu option called "Uniforms"
From this new menu click "Create Uniform" and name your outfit. Exit this menu and then re-equip the armour with the broken visual. Back out of that and go back into the new uniform manager and then simply click the uniform you created.

Et viola! You've got your outfit back.

It's a bit of a long work around, as opposed to just going into the .ini file and making your fixes there, but the Uniform Manager mod is worth having.