I agree that there are certainly legitimate uses for cars. But many countries in a cold climate manage by with more biking per capita. I would say it makes people mobile for longer and the grandma (up to some higher age) would just ride her own bicycle. The turkey will fit on your rear basket no problem. Jenny could also ride a bike home, because she has the school close.

It is of course only applicable in an urbanized area (even small cities can and do work like that). Not all the time, but below-freezing does not by itself mean prohibitively cold. Urbanized area means it is never near-total darkness for good and for bad.

I have picked my daughter up from her dance lesson my on my bike. She is a bit heavy in the trailer, but I'm not in a hurry and I refuse to but the type of laze person who drives 1.5 miles. (though now that it is cold...)

No, you wouldn't. Quite right. In the same way you wouldn't use a car to cross the ocean to grandma's island or trawl for fish. Other solutions exist.

But there's no ocean around most people's homes. Cold cities are very usual. Telling people living in them they should bike is just insensitive to them.

Of course, there are very cold places where much of the population happily bikes. See here for example: https://www.youtube.com/watch?v=Uhx-26GfCBU&t=800s

Much of the population? I live in one such place with many bikepaths and bicycling tradition where some people bike even in winter despite it looks just like on the video, but I've never seen old people risking it - for good reasons, as falling down can be deadly for them. My own grandma wouldn't be able to get anywhere the public transport doesn't go (many many places even in an EU country) - and she's one of the more mobile, more motivated seniors there. The others would be fucked.