Overall, we're not trying to force you and everyone else to cut over to bikes tomorrow, since for those individuals like yourself, your environment doesn't support biking at all. Hopefully though, we see a greater focus on building environments where biking does make sense, and less on car-centric living. However, to break down some of the specifics you mentioned:
The average low in Austin Texas is 43°F with rare dips below freezing (32°F). Looking at the temperature history for the last winter, Austin saw temperatures drop to freezing on 7 days during December and January[1]. When it's not freezing, at those temperatures, you can absolutely ride a bike safely and comfortably (though you'll need to put on some extra clothing to stay warm). As for your other questions:
> What risks should my very pregnant-for-the-last-three-years wife take?
She should take the risks she feels comfortable taking. In the opinion of me and my wife (we live in Seattle), we'd feel quite comfy biking in your city (as long as the paths are safe) during any of that weather as long as it's not freezing. If it was freezing and we knew we needed to go somewhere, we'd take a fatbike[2] (yes, that's their unfortunate name, and they work great in snow and ice with their huge tires).
> What if we lose a child or for that matter _her_ because she slipped on the ice?
That would be tragic, but ice means we all take that risk every time we travel by bicycle or by car. Driving a car on the ice is dangerous, even if driving feels safe and familiar. Thankfully, traveling on a bicycle means you're traveling at lower speeds, so should an accident or slip occur, the likelyhood of serious injury or death is far lower than at high speed in a car.
> How is she going to get groceries for our family of five-soon-six from the grocery store that is miles away from our house?
Cargo bicycles[3] make getting groceries, even lots and lots of groceries, even transporting small furniture, easy! However, you living many miles from a grocery store does make this all more difficult; I realize that where and what type of housing is available isn't totally up to you.
Baked into your comment is the statement of some real facts: that bicycling infrastructure isn't well developed where you live, the entire environment of where you live is built around making transport by car the easiest and often the only available option, and if you tried to adopt it personally now, it would be unfamiliar, dangerous, slow, inconvenient, etc. I think you're right that all those things are true. Trying to convince folks that they should bike to the giant Walmart that's 10 miles away for their daily groceries in the same way they might via a car, that's probably not going to go well, and I don't think it has gone well. That's why most of the constructive discourse I see, like the original article, is focusing on reshaping urban infrastructure around bicyling since that's where the density is. Hopefully we see that happen, and hopefully in the coming decades we see a reduction in investment into car-centric living (huge car-only suburbs with only homes and nothing to walk to for miles around), and an increase into more modest walkable suburbs with greater support for mixed use land (closer grocery stores) and the higher density housing (smaller lot sizes and smaller homes) which provide enough density to support the businesses in those walkable areas.
[0] - https://weatherspark.com/y/8004/Average-Weather-in-Austin-Te...
[1] - https://www.wunderground.com/history/monthly/us/tx/austin/KA...
[2] - https://en.wikipedia.org/wiki/Fatbike
[3] - https://en.wikipedia.org/wiki/Cargo_bike