A cold rain with the temperature just above freezing always seems to feel colder than snow with the temperature just below freezing. My guess is that there are at least two reasons for this:

1) The evaporation of water produces a cooling effect, whereas snow, as a solid, simply falls off (minus the smaller amount that melted upon contact). Rain falling on your hand with a temperature of 35 degrees is an extreme version of the chilly experience of coming out of a swimming pool on a mild or cool day.

2) Snow is pretty, while cold rain is not. Snow can make people more upbeat and thereby distract them from the actual temperature. There is nothing upbeat, however, about making your way through the coldest possible water.