I would disagree, in the sense that I don't think one can automatically derive the mechanics of skinchanger from those of heartbeasts. For at least three reasons:
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The skinchanger effect is closer to that enacted by Hermetic spellcasting than that enacted by a Heartbeast, and Hermetic spellcasting does allow minor stuff to change along.
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Having a Heartbeast is generally superior to being a Skinchanger. Since they are both Minor Virtues, you might want to give Skinchanger a little slack and allow clothes to change.
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For what it's worth, in old editions of Ars Magica shapeshifters' (N.B. not skinchangers', but still...) clothes and small items did explicitly change along.