From the Visit Svalbard website:
All guests with a foreign citizenship MUST bring their passports or national ID-card.
The website of the Governor of Svalbard says:
Everyone may, in principle, travel to Svalbard, and foreign citizens do not need a visa or a work or residence permit from Norwegian authorities in order to settle in Svalbard. Foreign citizens with visa requirements to the Schengen area do, however, need a valid Schengen visa if they travel through Schengen on their way to or from Svalbard. It is required with two entries in the traveller's visa to be able to return to the Schengen area (mainland Norway) after the stay at Svalbard.
(note: most of this doesn't apply to you, because as a Romanian citizen you have no visa requirements to enter the Schengen area)
and also says:
According to the Schengen regulations, all passengers passing through a Schengen boarder shall be controlled. Since Svalbard is not part of the Schengen area, everyone travelling between Svalbard and the Norwegian mainland must be controlled.
This section concludes with a link to more information from
the Norwegian government:
Since Svalbard is not part of the Schengen area, anyone travelling between Svalbard and the Norwegian mainland must be controlled. From 1 February 2011 travelleres will be controlled both at entry and exit.
Passports or national identity cards will satisfy Schengen regulatory requirements for identity verification.
Your national ID should be fine.
(Although if you have some specific reason for believing that your situation is different from that with a Dutch ID card, you should explain why so that people can verify.)