What Biden has not done: stop issuing drilling permits or impose export restrictions on fossil fuels. The former has some serious limits because of how the courts treat the right to drill as a property right once you hold a drilling lease, and the latter is simply untested.
I don't think that's ever been in serious doubt; the same simulation mechanisms used to produce climate modeling were used to figure out that nuclear winter is an issue in the first place. It's just that most people would prefer to address global warming without mass murder.
That doesn't actually work. Nuclear winter is caused by the stuff which gets mixed up with the blast. Hit Antarctica and all you get is water.
On top of that, it's where air descends from the stratosphere, so whatever particulates you do generate probably won't achive worldwide distribution at significant concentrations
Water in the admosphere is an extremely strong (but short lived) greenhouse gas.
And while it was hit, it could also be irradiated. While a nuclear blast has less radiation impact than a nuclear plant burning, throwing many nuclear bombs in one place may have other impacts. Contaminated water can be assimilated by living things.
And while in the body, it can do damage.
There's also more freshwater in Antarctica than in the rest of the world. Quite a waste, and enough of it to contaminate every source across the planet.
There is, of course, the possibility of geoengineering with sulfur dioxide. Sort of a nuclear winter without the nuclear. It's the same mechanism by which nuclear would and volcanoes do cause climate cooling. Not very safe but it may be in our emergency bag of tricks.
Wasn't there a proposal to do something similar by using ships to blast saltwater into the air? All the cloud coverage and reflected sunlight, none of the acid rain.
I think that's actually relatively low-risk to do as well (as far as experimental geoengineering goes). A significant portion of the warming in the North Atlantic has been attributed to lack of sulfur emissions due to changes in requirements for container ship fuels. Should be able to get a similar effect with just water with the effects being understood well in advance.