Rainbows can occur any time of year, as long as there is sunlight and water. The sunlight is the refracted and reflected by the water droplets.
The reason we don’t see as many rainbows in the winter has a lot to do with the type of rain we see in each season. Our rain in the winter is usually stratiform.
Stratiform clouds cover a large horizontal area, meaning it meaning it’s generally cloudy everywhere, and thus you’re missing one of the two rainbow ingredients, the sun.
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This is also why winter rain is usually more consistent in intensity than rain in the summer (and the rain yesterday.) Summer rain, and our storm yesterday, was convective, meaning there’s vertical development (think cumulonimbus clouds).
Because convective clouds don’t completely blanket the area, you can get sun along with rain, and rainbows.
Oh, and don’t forget, you can get rainbows during snow, too.