https://en.wikipedia.org/wiki/Westerlies This page states that the pressure over the poles is lower during Winter causing stronger Westerlies:
"The westerlies are strongest in the winter hemisphere and times when the pressure is lower over the poles, while they are weakest in the summer hemisphere and when pressures are higher over the poles."
On the same wikipedia page, it states the claim I am asking an explanation for: " This occurs when the Arctic oscillation is positive, and during winter low pressure near the poles is stronger than it would be during the summer
I would like an explanation of this phenomenon, ideally explaining why the polar pressure varies to such an extent...
Also, I would like to know if the logic I have used to reach these conclusion is valid
The jet stream acts as a barrier, dividing the warm and cold air masses. The Temperature will keep getting lower which will also increase the pressure and temperature gradient. In return the barrier (jet stream) gets stronger. This positive feedback mechanism remains until after winter solstice. Then the radiation reaching the pole will increase again, warming the air masses. Which will then lead to a weakening of the gradients.
So summarizing the above one could say, the missing radiation cools the air leading to a low pressure system at jet stream level. The jet stream itself gets stronger as the temperature gradient increases and acts as a barrier for warm and cold air masses and therefore maintains the pressure difference.