Very Much the opposite.
The ones tested in Bikini etc were larger than in use today.
Some as big as 20MT, nobody has anything in use (deliverable) bigger than 10 MT most today are much more accurate and therefore typically 1MT or SMALLER, Minuteman III is 300kt or .3MT.
Some U.S. submarine warheads are 1MT size, again most of our stuff in use (not in storage) is 1MT or less mostly less.
The Russians are usually a little less accurate and therefore a little bigger.

Nukes while terrifying are survival-able except for the inner most radius of action, typically the 99% dead zone is a couple of miles only.

While I hope none of us ever finds out, people would survive.
The oft retort of kissing your A** good by or everyone will perish is a myth.

Some soldiers were less than one mile from test in the desert and while many had health problems, none died directly as a result.

There is DOD footage of a unit of soldiers climbing out of foxholes and advancing, with the mushroom cloud rising in front of them. No special gear, just GI uniforms, rifles, steel pot helmet. Many of these are on the web.

A small percentage did suffer medical problems, but again not more than a couple of percent.

I sure don't want to minimize the downside which is awful, but if you are in a city somewhere and a strike happens, don't give up, you are not toast unless you panic.
As always in any survival situation, knowledge and will to live are the key ingredients.