In a world where some nations with nukes have veto, I would say that as soon as the war started, UN is pointless.
What about units that were on active duty around the world? Or after the nukes stop? Do you think there would be any appetite to try to help rebuild infrastructure, from a UN perspective, or would that just be left to individual nations?
So I think other posters pretty much settled that there wouldn't be any "UN forces" at play in Europe (or really anywhere in the aftermath of the Twilight War's nuclear exchanges). European units were committed to their home countries in a "total war" scenario. And really, in the alt history, who knows what the UN's "standing" as a "security" force would have been after Mogadishu (which might've happened in the alt timeline?).
I presuming you aren't looking for a UN cavalry to show up and somehow save civilization, specifically; but are more curious about how the world order might be rebuilt in the Twilight War's aftermath.
It's interesting, in the original T2K timeline, France abandoned NATO and made it through the Twilight War relatively unscathed (which was instrumental to the "Great Game" GDW played to grow out its 2300AD or Traveller 2300 universe where France was a key space power). But in Free League's edition, France stood along with NATO and was brought down like the rest of Europe, but slightly better off than other NATO powers. The Middle East goes a little different, in the original T2K there was a whole RDF Sourcebook describing a war still being fought between the US and the Soviets and the remaining powers in the Middle East at a full "modern" tempo because of the relatively easy availability of fuel, particularly aviation fuel.
Given the state of the U.S. and Europe in the aftermath of the Twilight War, you might have some NGOs out there, but with no resources to draw upon from their former international sponsors or private philanthropy. The only exception I could see is China (and pausing for a second to mention the Korean peninsula as a wild card in all this). Twilight War is still in the wake of Tienanmen, I"m not sure what footing China was on globally. In our real timeline, China made much more humanitarian and international development overtures in the world sorta in the background of the U.S. GWOT ... with Chinese benefits being access to natural resources particularly in Africa. Of course those resources were necessary to sustain China's role as trading partner with much of the rest of the world, so it's unclear how China would have acted in the Twilight War with all its major trade partners largely destroyed.
Broadly, I think we're left with a scenario similar to GDW's 1st edition 2TK to Traveller 2300 Great Game. "The great powers" of the world can't help with famines and plagues that are in many ways the consequences of the Twilight War. Everyone pretty much bootstraps for at least a decade or two, colonial ventures and other "partnerships" develop and a very different international order is established over a long 21st century.
T2K has always been a bleak, game of forlorn hope. I don't think the Free League updates it to anything more. I mean the fidelity to the original despair bleeding art direction is murmuring as best it can "this isn't going to to end well (at least in this century)."