Hi Samantha,
First, I'll explain in general where can you find that Alif. That Alif is found in indefinite nouns and adjectives, when they are in the accusative case. In case you don't know the accusative case, you can think of the "object" in the English sentence.
e.g : قَرَأْتُ كِتابًا = I read a book
Note that in this sentence the word كِتابًا is the object of the verb قَرَأَ, and also indefinite, that's why we must add that Alif we spoke about earlier. (كِتابًا pronounced ki-taa-ban)
What you need to remember is that Alif is NOT a long vowel.
Another example : أَخَذَ الطَّالِبُ قَلَمًا = The student took a pen.
The same here, we have the word قَلَمًا indefinite, object of the verb أَخَذَ, that's why we must add the Alif.
Now, moving on to the sentences you asked about :
Let's take the sentence without كانَ or سَيَكُون :
الجَوُّ بارِدٌ : This is a nominal sentence, and has two parts : Subject (= الجَوُّ) and predicate (or information) (بارِدٌ)
When we introduce كانَ to the sentence, it changes the predicate (which is بارِد) and make it in the accusative case. That's why we have
كانَ الطَّقْسُ بارِدًا / سَيَكُونُ الطَّقْسُ بارِدًا
Remember, the Alif for the accusative case will be applied to all the predicate part of the sentence, even if we have adjectives and nouns
e.g : كانَ الرَّجلُ وَلَدًا صَغيرًا