The issue with the articles is interesting. Let me give a try:
Er hatte die Mütze, den Mantel und die Stiefel an.
The articles clearly indicate that you are talking about very particular pieces of clothing. Not just "some hat" but "that particular hat".
Er hatte einen Mütze, einen Mantel und Stiefel an.
The opposite, all nouns indefinite, and probably very normal.
Er hatte Mütze, Mantel und Stiefel an.
Now I speculate. I think the nouns here are turned into uncountables, like you do with "Zucker" or "Honig". The sentence seems to focus on presentation of the person as a whole, and the items are reduced to their function. A similar sentence is:
Er trug Uniform.
The sentence does not indicate that he wore that particular uniform, and it does not merely indicate that he wore any uniform, but rather the sentence focuses on the social function. Like:
Er trug Uniform. Er kam nicht als Zivilist, sondern als Armeeangehöriger.
I think it is specific to clothing, make-up, and similar things. I do not recognize any general grammatical rule.