In my fictional setting, the planet that people live on, called "Nearth" has one smallish very dark moon close in, and a large moon farther off with a very high albedo.
Nearth is exactly the same as Earth, with exactly the same sun, orbit, mass, radius, etc.
The large moon (Saur) has 1.5 times the mass and 1.17 times the radius of our own moon.times as large as our own moon. It orbits at 68 Nearth radii, or 270000 I'm, or 1.13 times the Moon's distance from Earth. It has 0.93 times the density of our own moon.
The tiny moon, (Oun), is 0.55 times a large as our moon, has 0.17 times the mass, the same density, and orbits at about 40 Nearth radii, or 158000km, or about 2/3 the distance of the Moon.
What conditions would be necessary on the large moon so that it has a high albedo? I considered clouds, but the moon is far too small to hold onto a sizable atmosphere (I believe). That leaves me with ice of some sort.
What conditions are necessary for a moon with the specifications I have given to maintain a layer of ice on it's surface over astronomical timescales?
The ice arrived as a large impacting body from beyond the frost line.