Had an important realization yesterday, during a discussion on a different prayer. Per the FAQ, the re-rolls from the Hammer of Sigmar prayer can NOT be used to re-roll the impact hits or horse attacks from the War Altar.
"Because the rider and mount can be hit separately, any saves and other special rules of the character (including those from magic items, spells, etc.) are not passed to it mount, and viceversa."
Feel free to look up the full passage in the FAQ, and be aware of this during play. The War Altar is good enough already, we don't need to be taking things over and above that aren't deserved.