Using לכן in place of אז here would sound too formal and written ?
( Or לכן has a slightly different meaning/use ? )
It would be too formal and written, that's true. Whether the meaning would be slightly different? - I feel that it would be very slightly different, but I'm not sure all native speakers would agree.
Yup. My question too.
Is there a reason for the word order? Why מתקרר בחוץ and not בחוץ מתקרר?
I also have a question regarding the word order.
Why not בחוץ מתקרר? I think it should also be counted as correct.
I agree. It should be accepted.