Yes. My feet hurt the night when I walk barefoot in my house on a cold day.

Yes. Cold, and pressure changes can be very painful.

Yes, cold would constrict muscles ,unlike warm temperature where they wouldn’t and be more relaxed.

Yes.

It is said that the weather is a good barometer for your joints. Changes in barometric pressure affect how your joints feel. Ever hear someone say their joints tell them a storm is coming?

Well, I lived in New England until I moved to California at age 30. I’m more than twice that now. I have all kinds of aches and pains. But some things hurt my young body in that steely winter cold back East that have never hurt since; in particular, the site of my knee surgery at age 27. So I’d say yes.

I would think so. If the room is cold eventually your body will get colder and your muscles will contract and cause pain. Think of when you are swimming in cold water and get a leg cramp. Of course, other things can contribute to making it worse. Like being low on electrolytes and dehydration or as already mentioned barometric pressure changes or having a physical ailment, like arthritis or gout or poor circulation.
It’s why a lot of old people move south as they age.
Heat helps to relax muscles and joint.

According to my wife, it does. She has an old shoulder injury, the result of a previous marriage with an abusive ass hat who would beat her. In warm weather she generally has no problem with it, but when the weather turns cold it always starts giving her problems. Been going on since before we met, and we have been together 40 years this June. So yeah, I think cold weather can have an effect in those situations.