Exactly what it says on the tin: if you're for whatever reason unhappy with the default Skyhold pajamas, you can pick a replacement more to your liking.
Or, if you are unhappy with the formal wear and can't (Trespasser DLC) or do not want to use the Invisible Formal Attire mod, you can pick one of the formal attire replacements.


Update
Uploaded file with multiplayer armor replacements (those that don't have questionable headgear on them). Multiplayer armors require no DLC but are race and gender restricted - details below.

Uploaded file with several DLC outfits. Take note: the mods changing the pajamas into DLC armors will work only if you have the corresponding DLC.

Uploaded a tutorial and templates for making your own variations of wearable singleplayer armors into your Skyhold outfit or into the formal attire.
(tutorial doesn't cover multiplayer armors - for them the process is completely different).
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Who can wear what:
All singleplayer armors work for both genders and all three classes.

• The Dalish keeper, Dalish scout and Dalish warrior armors are elf-only.
  
  
• Carta coat and Legion of the Dead armor are dwarf-only.
  
  
• Adventurer armors, light, medium and heavy, are human-only.
  

• Inquisition light, medium and heavy armors work for everyone except qunari characters.
  

• Warden light, medium and heavy armors also work for everyone except qunari characters.
  
  
• The Apprentice coat, Enchanter coat, Hunter coat, Prowler armor, Defender coat and Vanguard armor suit everyone.
  

• DLC outfits work for everyone (with the exception of the dress which works for female characters only), assuming you have the actual DLC that contains them.
  

 
  
All multiplayer armors are restricted both by race and gender:

• All three of Isabela's outfits, Assassin's mantle, Templar's regalia and Necromancer's Inquisition warmage robes are for female human characters only.
  

• Elementalist's robes are for male humans.
  

• Multiplayer Arcane warrior armor and Arcane Warrior Inquisition warmage robes are for male elves.
  

• High keeper tunic is for female elves.
  

• Silent sister cuirass and Silent sister proving cuirass are for female dwarves.
  

• Deathbringer hide and Arishok pauldrons are for male qunari.
  

• Isstaaras-Saar is for female qunari only.
  

Known side effects:

• Some armors can and will behave strangely in some cutscenes they were never meant to be in.
  

• This mod does not affect the appearance of your companions in Haven/Skyhold. However, since it changes the entire unequipped appearance file, when stripped of their armor outside of Haven/Skyhold they will be wearing their own versions of the appearance you picked in the exact same colors. (If you choose a race-specific armor, your armor-less companions will turn into floating heads). Same goes for the formal wear replacements - the formal attire for companions will turn into their version of the outfit you picked.
  

Compatibility:

The skyhold outfit replacements are compatible with InvisibleFormalAttire, as seen in the dalish armor screenshots. If you wish to wear your chosen armor at the Winter Palace, you'll need to install it.
Similarly compatible with Invisible Starting armor.
This mod  should also be compatible with various retextures as much as the armors themselves are compatible with retextures. If you, for instance, are using a retexture of the pajamas you'll still see it under the coat in apprentice/enchanter armors.

The formal wear replacements are for obvious reasons incompatible with Invisible formar attire.

The skyhold outfit mods aren't mutually compatible - if you install multiple files at once one will overwrite the rest.

Skyhold outfit and formal wear replacements however are fully compatible. You can install one of each.

How to use:
Pick one .daimod file from the archives for the skyhold outfit (and/or one for the formal wear).
Install/Uninstall using DAI Mod Manager.
Enjoy your game.

Many thanks:
To the creators of the toolset over at daitools.freeforums.org – for making an unmoddable game moddable.
To modder Toloc - for proving this can be done.
To modder Dheuster - for providing means to use the replacements in Halamshiral.
To modder borglet - for the appearance hashes tutorial