It's a great idea, though it would take a lot of training for me to learn how to make all that. Would be great if there were at least partially pre-built components. Example, an LED, phototransistor and counter all together with an I2C output. Connect 3 or 4 wires to a Raspberry PI, execute a script and numbers are flowing on the screen. The more "plug and play", the better. I'm just not mechanically and tech savy enough to know how to source all kinds of random components, what specs they need to have, wire them all together in the proper way, make them all communicate with each other, etc..The wheel can move slowly. Every time a beam is established there's one clock pulse. You don't have to spin it like a top.
The approach I'm envisioning is having the sensor and wheel. Those wheels come in many configurations. The illustrations have 33 to over 50 windows. You can get them with hundreds of those marks. They're much smaller.
So the wheel slowly rotates as the weight of water in the bucket opposes the spring tension. As the weight increases you get a pulse every time a window opens. The electronics would consist of something like a decade counter and an encoder that would produce digits. For higher number counts you would need two decade counters and as many encoders as digits you want. Or, since microprocessors are NOT my forte you could program a controller to count the openings and give you a readout. When the bucket is drained you can disable the counts until the bucket has fully emptied and the weight of the bucket has returned to the zero point. OR you can use a large enough capture vessel, one that won't need to be reset until rain tops 20 inches. When the storm is past you reset the system and measure again.
Not having to empty until the rain is over would be a plus. That would prevent the need of the top solenoid.
Weight of the snow pack is all I need directly from the rain gauge. Snow depth on the ground would be obtained through a different method and a script would combine the values to determine snow depth to liquid ratio.As for measuring snow - that's a whole different animal. Or maybe not. If you're measuring the weight of the apparent water weight then inches of snow won't matter to you. 10 inches of snow can have the same weight as 1/4 inch of snow. Just depends on how wet the snow is.