According to the UK Met Office winter rain normally falls as conditions become warmer and in summer, when conditions become cooler. This is probably due to warm and cold fronts moving across the land mass.
Rain Is Usually Cold: As rain falls from a higher and colder altitude it is usually cooler than ambient conditions at ground level. The very act of falling may further reduce the droplets temperature as it falls through air with less than 100% humidity, where wind chill increases evaporation from its surface, cooling it quickly by removing the latent heat of evaporation.
Rain Cools Us: When the droplet reaches us it cools its surroundings. Water absorbs a vast amount of heat as it has a high specific heat capacity (about 3 times that of iron!) drawing heat out of the atmosphere and anything else it contacts.
Increased Humidity Can Make The Air Feel Colder: As the rain water warms it begins to evaporate, increasing the humidity of the air which correspondingly loses its ability to insulate - the air its self begins to feel cooler.
All this without your clothing actually getting wet!
(100% humidity can prevent sweat from evaporating, so you feel clammy when working hard or if ambient temperatures are tropical: Humidex Table)