I was starting to feel a bit chilly when I first read this and would probably have written “Non ho piani (o niente) per oggi” but addosso evidently can mean “on”, “take upon oneself” or “charge with” ecc. So easy to confuse with indossare when reading quickly 
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In Tatoeba you can find two sentences with non ho indosso as close matches to your original sentence. So, yes, Floria7 you might get chilly!
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I think your first thought might have been correct, WordReference suggests
have nothing on informal (be naked)
non avere niente addosso
Don’t come in! I’ve got nothing on!
Non entrare! Non ho niente addosso!
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Confusing sentences: I’m reminded of a Christmas in Minori when a charming American lady, pursued by our amorous coach driver, kept shouting “Avanti avanti!” (Go away, go away!) when he knocked furtively on her door at night. When all was explained, everyone laughed, even the coach driver tho’ he said he had been very confused and not a little bit hurt. Ah!
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