Saturn's rings are made mostly of ice and rock fragments orbiting the planet. Earth could possess a ring system in principle, although the debris would have to occupy stable orbits and survive collisions, radiation and gravitational perturbations.
The sky would change first
From the surface, the rings could form a bright band across the sky. Their appearance would vary with latitude and the ring plane. Near the equator, the rings could appear as a broad strip; from higher latitudes they could look narrower or even be difficult to see edge-on.
More light at night
If the rings reflected substantial sunlight, they could brighten nights even when the Moon was below the horizon. The effect would not be uniform: the ring material would be lit differently depending on the Sun, the observer and the ring geometry. Night ecosystems that evolved without such a permanent structure could respond strongly to the new light cycle.
Would Earth get colder?
Potentially, in some configurations. Rings can cast shadows, reducing sunlight reaching parts of the planet at certain times. Whether that would produce a meaningful global climate change depends on how much material the rings contained, how opaque they were and how their plane was oriented relative to Earth's orbit.
There is no single climate outcome for an Earth with rings. Ring mass, optical thickness, particle size and orbital geometry would all matter, so claims of one precise temperature change are unjustified without a specified ring system.