dim at night

I unusually woke up around 3 a.m. and found the outside was not very dark. I felt awkward and looked for the reason.
Moon couldn't be there, because it was raining last night and supposed to last til next morning. I wonder if it stopped raining and moon came out, and it could have snowed and the snow might have covered the ground, so the moon light shined and reflected. As I was thinking, you know, I fell in sleep.