Is it acceptable to surface run network cable outside to get between
floors?
If I do this, should I be using shielded cable?
Looking at networking to a ground floor extension where internal routing
is
not an option..
Outside run will just be 4m vertical. Total run length about 20m.
I know this is done with satellite cable although I try to run concealed
as
far as possible.

get a wireless router? Prolly end up about the same cost when you take into
account time and materials?