Plane: We're talking about commuting here. And good luck getting on a plane nowadays as an adult without a license.
I've never used my driving license as ID for boarding an aircraft. Other forms of identification are available. Do you really think that people that don't drive also never fly??
Trains can take you between towns, not just across them.
Snow does not preclude bike riding.
Other than for commuting, taxis are cost-competitive to car ownership in the UK. They're frequently less convenient, but not more expensive, especially if you live in an urban location that lets you use public transport for a proportion of your journeys.
I appreciate you're playing devil's advocate but the barriers to not owning a car aren't insurmountable, even in the US. As someone else in the thread suggests, learn to drive safely or move to New York.