Snow doesn't come in the form of frozen raindrops because it was never rain in the first place.
During the winter in temperate climates, there are no raindrops in the clouds. Instead, a cloud contains a mixture of supercooled water droplets and ice crystals. The droplets evaporate more quickly than the crystals sublime, so over time water vapor evaporates from the droplets and is deposited onto the ice crystals. This causes the crystals to grow. The exact shape of the crystal depends on the temperature and humidity in which the growth occurs, but in general respects the hexagonal crystal structure of ice. The crystals can also stick together or stick to water droplets (which freeze when they contact the crystals). Eventually they become too heavy to be supported by the updrafts in the cloud and fall as snowflakes.
If the temperature near the ground is above freezing, the snow will then melt to form rain. Of course, once a snowflake melts, it loses its crystalline shape and becomes just a blob.
Sometimes frozen raindrops do fall (called "sleet" in the US and Canada and "ice pellets" elsewhere). This happens when snow melts into rain on the way down and then refreezes in a cold layer near the ground. This results in frozen blobs shaped roughly like raindrops, just as you would expect.