"I wonder how the barometric pressure changed during that time."
It's possible it changed a bit, but it's possible it changed very little. I as guess, I would say it would probably be less than 1/2" of mercury and it's possible one could more changes in pressure on day without such high differences of temperature.

"According to the laws of physics, the colder air has greater density, therefore greater weight, so the barometric pressure should have gone down during the time that the air was getting warmer."

Say, you a big walk in refrigerator and a big walk in oven both have a door open. Say one is -40 C and the other is 200 C.
The air pressure is either won't be any different. The air density will be different.

In terms of weather it is the opposite that you describe, large warm regions have and are called high pressure regions and cold and moist regions have and are called low pressure regions. With a barometer, it's use is to predict weather- rising pressure generally indicates future warmer weather and dropping pressure indicates a bad weather is coming. Barometer purpose is predict changes in weather, but doesn't tell you much about present weather [though a very low pressure indicate you are near the center of a hurricane- in case didn't notice the cows and rooftops flying by you].