About as secret as the fact that Israel has nukes.
Nobody formally admits to anything, but if you read between the lines of publicly available information on budget allocations, equipment purchases, what facilities are built and maintained, what versions of certain jets, planes etc a country has or buys or builds an expert on the matter can tell you down to the most minute detail what nukes a country has or houses.
It's the kind of "secret" that's public knowledge with plausible deniability (in order to not have to sign up for international non proliferation treaties etc) where you actually kinda sorta want people (especially possible enemies) to know you have nukes as a deterrent.