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So if both players have Daemons, and there is a friendly and an enemy Pink Horror unit next to each other, what happens when each unit has a Hornblower and an Icon Bearer?

Icon says if the unit rolls a 1 for battleshock, the unit gets d6 Horrors added to the unit. Hornblower says enemy units w/i 6" that roll a 1 for battleshock have to reroll.

If my unit of Horrors rolls a 1 for battleshock but must reroll, does the first roll of 1 give me d6 models back? Or does the first roll not count because it must be rerolled?

Link to battlescroll

That one doesn't register because it needs to be rerolled - the rule is, in the four-pager, that rerolls occur before modifiers, and for the lack of a better term, I'd say the recouping D6 models is a "modifier," in that it's an additional bonus based on your original roll.
That's how I would interpret it, but honestly I don't have the hard rules to argue it.

Common etiquette would imply that the original roll is discarded. Otherwise the hornblower could create a scenario where a unit has both passed and failed their bravery test.
So, I believe if you rolled a one, you would have to discount that result and reroll.