The Iceheart outfit style (from the consumable motif)
does not have the same dye channels as the actual monster set item.
The ice portion of the actual equipment piece—which covers your characters face—will accept a dye colour. However, on the outfit style variant, the ice portion is completely non-dyeable and thus will always retain its default appearance. You can clearly see the discrepancy between the two in the comparison below:

(actual equipment on left, outfit style on right)
This completely changes the usability of the outfit style variant, as you can no longer recolour the mask to give it the appearance of a different material—as I've done if the left picture, turning it into a dull-grey metal that complements the rest of my outfit. On the other hand, bright, gaudy ice does NOT match a whole lot of things. I believe the issue lies with the 3rd (from the left) dye channel on the outfit style. The first two channels work fine and dye similarly to the actual item, but the 3rd simply does nothing at all, and this might be why the ice portion can't be recoloured.
I spent 180k on the motif thinking I would be able to re-create the look I achieved with a 1pc Iceheart mask in the past, but now realise it was a complete waste of gold and will never be using it in its current state.
@ZOS_GinaBruno,
@ZOS_JessicaFolsom, please look into this issue.
PC/NA — Daggerfall Covenant — BGs, Kaalgrontiid
Kalazar Chalhoub — Redguard Nord Stamplar
Kalaron Caemor — Altmer Magsorc
Kalahad Cirith — Dunmer Magden