With the One-Country-Pass you can only use trains in that specific country. So you would have to buy a ticket from Cologne through Switzerland to the first stop beyond the Italian border. With a global pass you have one trip from your home country and another one back there free. As far as I know it is important, that you have to use two of your travel days if you change trains after midnight on a trip, that started before midnght. The Nightjet from Cologne starts at 23.53, so you would have to use two traveldays for the trip to Milan.

Assuming you have a global pass there are a couple of errors in the above reply:

Firstly I am unsure why you need to travel by an extremely expensive routing for reservations when there are many daytime routings available. Min 16 euro in a seat on the nightjet, over 70 euro for a shared couchette and even approaching 200 euro for a cabin,  then  another 26 euro on Eurocity.

Ther are many daytime routings from zero reservation fees and max 20 euro including some overnights not on a sleeper train.

If you do travel by the 2353 from Cologne you only need to set your journey to change at Basel SBB (Not Basel Bad. Basel SBB is in Switzerland so you have left Germany on a train scheduled before 2359 and a further In/Out day is not needed to Milan. 

There is plenty more advice from community members.

Thank you for the correction.

This NJ is combined-for administrative reasons, to 3 seats cars-old IC, that are labelled as IC and do NOT even need a RES-as any ICE by DB. In fact you cannot even RES as seat-only via bahn, but can do via oebb-and these seats are not labelled as such, so you will get discussions by those who sit there.

To make this trip with that start you need to use 2 traveldays anyway.

IF you go in aug and IF you want to save money-be smart: board it in BONN > 0.00=next day and go there on an RE with your 9€-and be even smarter to know he eternal delays on DB. Vorher konnten die Passholdr das sogar ganz schlau selber bedenken…………...