Magic bow + other magic arrow Question

Magic Items

First time DM'ing so just want to make sure I get this right for my player.

He has a +2 Icy Burst Bow, fires a +1 flaming arrow. The damage is +1d6 cold AND 1d6 fire. Or just 1d6 cold because the bow overwrites the arrow?

Liberty's Edge

The attack would have +2 to-hit and Damage from the +2; it would have Icy Burst from the Bow, and it would have Flaming from the Arrow;

The attack would deal 1d8 Piercing, 1d6 Fire, 1d6 Cold, + Piercing (From Enhancement),and +X from the Composite quality (Assuming they use a Composite Bow)

TL:DR: The Weapon Magic Qualities will all apply from both sources and the attack gains the highest Enhancement Bonus between the Bow and Arrow.

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