Sorry, but this is a fundamental misunderstanding of the difference between rain and snow.
Rain is actually more immediate and flows to the drainages. Snow is more of a time released capsule that holds much of its water until spring, allowing the various damns and reservoirs to manage the flow. In terms of the higher elevation ecosysem, snowmelt is generally much more efficient at soaking into the ground than rain is.
Rain is like getting your entire yearly salary in cash on January 1st. If you aren't careful, you spend it all or lose it and once its gone, its gone. Snowpack is like getting a steady paycheck every two weeks throughout the year. It guarantees you have funds when you actually need to pay the bills in the summer.
It’s almost as if the Rocky Mountain West has an entire ecosystem evolved heavily around Winter snow pack. Deprive those mountain of that snowpack and the ecosystem starts to unwind. This is not going to benefit the animals that rely on that very ecosystem, whether that's up high or down stream. You start stacking year upon year of low snowpack and the effects will be entirely negative.