Line a standard 12-cup muffin tin with liners or spray with cooking spray.
In a medium bowl whisk together the flour, salt, baking soda, cream of tartar, granulated sugar, brown sugar, and orange zest. Set aside.
In a large bowl whisk together the eggs, buttermilk, oil, orange juice, and vanilla extract.
Add the dry ingredients to the wet ingredients and stir until just combined.
Add the pomegranate seeds to the bowl and gently mix together.
Spoon the batter into the prepared muffin tin.
Bake in the preheated oven for 22-25 minutes, until the muffins are golden and a toothpick inserted into the center of a muffin comes out clean. Let the muffins cool completely.
In a small bowl whisk together the powdered sugar and pomegranate juice until smooth.