We'd survive the first few months after nukes start to fly, after that I'm not so sure. The vast majority of humans live in areas where the climate and environment makes survival without a lot of cultural knowledge very hard. Add to that fallout, possible climate effects from the nukes, I can easily see a non-zero probability of total extinction within a couple of years.

Living in Seattle, I've thought about the odds of surviving a nuclear attack here. I figured surviving the blast is very possible. But after that, things look pretty grim. Long term survival in the city itself is improbable, and due to terrain there are only 3 ways out of the city. Consider that all the survivors would be clogging those routes to get to a farm, it looks like succeeding would also be improbable.

Your only hope would be to leave before the attack.

Seattle is just 20 miles from NBK as the crow flies. It's reasonable to assume the entire region will be carpet-bombed until completely sterile.

https://en.wikipedia.org/wiki/Naval_Base_Kitsap

"It is the home base for the Navy’s fleet throughout West Puget Sound, provides base operating services, support for both surface ships and fleet ballistic missile and other nuclear submarines as one of the U.S. Navy's four nuclear shipyards, one of two strategic nuclear weapons facilities, and the only West Coast dry dock capable of handling a Nimitz-class aircraft carrier and the Navy's largest fuel depot. Naval Base Kitsap is the third-largest Navy base in the U.S."

The entire Western WA metro area would be completely 100% screwed. You ain't getting over the cascades in a car. You can barely get over it on a regular US holiday. Going north? Yeah good luck fighting with the 10+ million Canadians trying to come south after their own inland routes are taken over by chaos. You could maybe go South and then inland up the Columbia, but then you'd have to pass through the radioactive wasteland that would be the bombed out Hanford reservation

I'm thinking of current subsistence farmers, specially in Africa and South America. Nuclear war has some impact, but I don't think all areas in world are heavily affected. I doubt absolutely all of these will be hit to extinction level. Developed countries on other hand surely massive starvation to boot.

I don’t believe there are any Southern Hemisphere nuclear powers currently. Would northern hemisphere powers deliberately target folks in the Southern Hemisphere? If not, I expect most of them would survive.

I imagine there would be plenty fish in the ocean still. Some would survive.