I spent the past year and a half parenting one, then two kids (now 1.5 and 3 years) mostly by bike. Here are some of my takeaways:
1) It’s totally doable for many people (depending on where you live and work, and other complications).
2) You may end up wanting to be more car-lite than you were before kids (many/most young kids hate car seats in various phases of their lives and scream while in them, and love box-bikes and buses and trains; also, biking may well be your only reliable way to get exercise)
3) You may end up wanting to be less car-lite than you were before kids (the tyranny of naps cuts up your day so much, it’s nice to get from A to B faster. Plus, getting car rides from friends when you have kids is pretty much impossible, and installing/uninstalling car seats in rental cars is a pain, and your time is at a premium)
4) Think through contingency plans. What if it’s too icy to bike but your work and daycare are still open? What if you’re sick? What if you’re sick like half the winter? (You may well be sick like half the winter)
5) Rewarding children is good parenting and preserves your sanity. Keep rewards at the ready.