Which characteristic of a planet covered entirely in bright white ice would shift its calculated habitable distance relative to the star?

It would reflect more stellar energy back into space, effectively making the world 'colder'

Modern calculations refining the Habitable Zone incorporate factors beyond just orbital distance and basic atmospheric composition, such as albedo, which is a measure of surface reflectivity. A planet covered entirely in bright white ice possesses a very high albedo, meaning it reflects a large percentage of the incident stellar energy back into space rather than absorbing it to warm the surface. This high reflectivity makes the planet effectively 'colder' than a dark ocean world at the same distance. Consequently, to maintain the minimum temperature required for liquid water, the habitable zone must effectively shift slightly inward toward the star relative to where it would be calculated for a darker surface.