Cold start problem x5 3.0i

[Frans]

Last few weeks my x5 doesn't start in the morning , it's freezing a few degree in the netherlands ( europe ).
It only happens with cold weather otherwise no problem ,the starter motor runs normally
I went to my BMW dealer and their diagnostic was a defect fuel pump.
They changed pump with no result ;also a new battery was placed but
problem remains the same .
I found on this site a few very detailed articles concerning the ignition
switch could this be the reason for this problem.
Is their a possiblity to check this switch or is the only way replacement.
Anyhow thanks for any information

best regards frans