the weather being cold, they went for a walk..................
-despite
in spite of
although
but

Despite the weather being cold, they went for a walk
لانه في حالة اختلاف الفاعل بين الجملتين لابد أن يتم ذكر الفاعل قبلv.ing

Thanks a lot you convinced me!

the weather being cold هى جملة غير منطقية لغوياً
و الاشكال الصحيحة هى
being cold weather
cold weather
the weather is cold
و اذا اعتبرت the weather being cold صحيحة فليشرح لى احدكم اركان الجملة و نوعها

فى نفس الجملة فى الصف الثالث الاعدادى وه despite my work being important

Despite the coldness of the weather , they went for a walk