I live about 8-10 miles from work (depending on which route I take). I ride my bike EVERY day. And yes, I live in a mountainous and very snowy part of the country. Riding a bike is far from free, but if it eliminates you needing a car (and car insurance and gas). If you can make a $750-$1000 investment today and have everything you need to ride year round it will save you oodles. If you are truly interested, I can put together a list of things I believe to be necessary and a luxury to make bicycle commuting comfortable and enjoyable. And, I am capable of putting a week's worth of groceries for my family on one of my bikes. Of course, I enjoy cycling and log about 5000-6000 miles a year.
On the used car front, it is possible to score a nice car for $2000 or so. My car is only worth about that. It has some dings and bumps, but nothing major and nothing you would notice without looking closely. It has mainly highway miles (at least 75%), 130k miles and is well taken care of. No weird smells, no rips in the interior and my spouse just finished replacing the hub assemblies and all 4 struts (no impact on value). And it has a trailer hitch.
I have no hesitation driving this car across the country with my family towing our small little trailer.