Weather may not be a very original conversation topic, in and of itself, but when writing, describing the weather sets the scene in a way that instantly correlates with emotion. Weather is mood. Here are some examples:
The sky was gray and gloomy and constantly dripping. It was the kind of weather in which old people complain of depression and rheumatism, and young people make faces at the sky and stay home by choice. It was cold and damp and even the small fire in the huge fireplace seemed like a hopeless attempt.
"Atrocious," Mr. Frederick said around the pipe clenched in his teeth. He was staring out through the drops covering the window at the grey sky and grey moor. "How long has the weather been behaving in this unacceptable way?"
His son Mark didn't look up from the book he was reading by the fire. "Over two weeks," he said shortly.
"That's what I thought," Mr. Frederick mumbled. He turned away from the window and pulled his old red dressing gown around his shoulders. He shuffled away in the direction of the kitchen and a hot cup of tea.
The snowflakes were white in the light of the street lamps, swirling and drifting down into the street to join the snow that was already heaped up on houses and frosting the empty branches of the trees. The couple walking along the street were so bundled in scarves and overcoats and hats that they would have been unrecognizable even to freinds. The girl threw her head back to catch a snowflake on her tongue. The young man with her smiled, but took her arm to hurry her along.
"Come on," he said. "We don't have time."
"I know," the girl said, but she stood there a moment longer, staring up at the sky where thousands of white flecks were whirling out of nowhere.
Ahead of them the sound of a train whistle echoed through the snow. The girl took a deep breath of cold air that tasted like snow and hurried after her brother.
You could also write something where everyone is happy to see the rain because there has been a drought, or a scene in which the snow is threatening instead of peaceful. In any case, the way you describe the weather, and the weather being described, can set your scene almost by itself. It's also fun to write about! I love thunderstorms especially. Lightning and thunder are like Drama Mix: just add water...