This one comes from Joel Dice, Thanks Joel!!
The first step in traveling by bike is finding safe, pleasant routes to the places you and your family want to go, such as work, school, and the grocery store. Ideally, this should be an important consideration when choosing a place to live, but even if you're already past that point you can pick up a map (such as the one published the Denver Bicycle Touring Club) at a local bike shop and use it to plan your trips. The best route is not always the most direct one, so you may want experiment with a few alternatives.
As for the bike, I recommend a solid commuting or touring bike with mounts for full-coverage fenders and front and rear racks. Once you add racks, panniers, and a bungee cord for the rear rack, you've got a lot of carrying capacity for groceries, extra clothes, or whatever else you might want to carry. Fenders are essential if you want to show up at your destination clean. Finally, if you ever ride at night, invest in a high-quality headlight, taillight, and reflective vest and anklets. A bright headlight that lights the way is essential for confident night riding.
For winter riding, I'm a big fan of GORE RideOn cable systems; they line your brake and derailleur cables end-to-end, so they won't freeze up in the snow and ice. I also prefer big, high-volume tires in the winter, inflated to relatively low pressure for traction. Some folks like studded tires, but I find they don't add much traction except on ice, which is less common than packed snow and slush on city streets. The important thing is to plan stops and turns well in advance, and consider just walking steep downhills if you're not sure you'll be able to stop before meeting an intersection.
When dressing for very cold rides, I really like big, thick mittens, so my fingers can share body heat. I'll also wear a breathable skull cap under my helmet, a neck gaiter to pull over my face, a few breathable top and bottom layers (including a thick washcloth tucked into my pants to insulate the male parts), a windbreaker jacket, ankle gaiters, and neoprene booties over my shoes. This outfit is comfortable down to -15 degrees, which is the coldest weather I've experienced.