Yes, weather is just a matter of gear, and these days the wet and cold weather gear is amazing. The best bike gear isn't cheap, but it's much cheaper than the typical repair on a car when something breaks. Panniers are an easy way to carry a lot of groceries with minimal effort. If someone has a huge family there are also cargo bike options. But, of course, with modern American cities, there might not be a grocery store in a reasonable biking range. There used to be mom-and pop grocery stores all over the place. And, in Europe it's pretty common for there to be a small grocery store within a 5 minute walk of your house.

But, North American roads are designed only for cars. Bicyclists and commuters pay taxes to maintain roads, but the roads are built for cars and trucks. To really feel safe on a bike, you need separated bike lanes. You build those, and people will use them.

In many places in North America, a bike lane is merely a thin strip of pavement that's centimetres from passing cars, and in the door zone of parked cars. Even in good weather that's dangerous. In bad weather it's truly awful. But, people still use those bike lanes. In fact, some people even bike and share the road with cars where the bike lanes don't exist. That should be a clue that people are dedicated to cycling, and if you built actual good bicycle infrastructure, a lot of people would use it.