Question

Car side mirrors do not work when they are covered with frost. What does frost do to the surface of a mirror to cause a diffuse reflection?

Answer 1

There are two related effects that contribute to this phenomenon.

Explanation:

Firstly, the frost makes the smooth surface of the mirror rough, meaning that parallel rays are reflected in different directions (the diffuse reflection that you referred to in the question.) A diagram might help:

Secondly, there are extensive and multiple refractions which cause the light to be distorted. This is the reason that frost looks white, whereas ice is clear (so called black ice, due to the colour of the road surface.)

I have never done the experiment, but I suspect the second effect is dominant.