Sure, you won't be able to make a measurable impact by yourself. However your mindset quickly leads to a tragedy of the commons type response that leaves us all in trouble. We should all take a more proactive approach to this in both our private life and in our professional work.
That is exactly the point of the analogy. One single snowflake doesn't prevent the avalanche and therefore one single snowflake is not to blame. However if enough snowflakes are removed the avalanche is stopped. Similarly no single person is going to fix climate change. The only way we see results is if enough people band together to make changes.
Tragedy of the commons is caused by regulation. That's how you get commons in the first place—resources that everyone is allowed to use but no one has any investment in. It's solved by allowing the commons to be homesteaded and converted to private ownership.