You're creating a lot of trouble for yourself if you try to correct those small errors (if it is an error, since that was what really happened). How would you go about to correct things if it rains the day after a snowfall? How would you tell it apart?
My advice would be to accept this small limitataion of your sensors capability and consider the rain value being, when water fallen from the sky reaches the soil in liquid form. At least that's what I do and we probably have a bit more of that white stuff falling down in Sweden. :)
If you need an absolutely correct mesurements of snowfall you need a heated rainmeter that melts the snow and also regularly make mesurements of the thickness of the layer of snow on the ground.
Hi P3R, I've been thinking about a heated rain gauge, but it would be very difficult for me and my two left hands :) I guess I'll have to except the wrong placed rainfall. We don't have much snowfall during the year here, so it wont be happening that much.
A lot of wx station owners in the states have been adding heaters to their rain gauges. The latest and most popular home-made design consists of a ~25W reptile heat cable wrapped around the underneath of the rain funnel and glued in place. Reptile heat cable is a flexible, resistance heater cord obtainable from pet stores and designed to keep lizard terrariums warm. Along with some insulation for the outer walls of the rain collectors and extension cords to power it from a house outlet, it is a pretty cheap and easy set up.
Some people have added thermostat power cubes to their installations to turn off the power to the heat cord when the temperatures are above freezing.