Do dark conditions due to high-altitude smoke prevent ultralights from flying?
The only regulations that apply to ultralights are in part 103. Apart from the obvious visibility and cloud clearance (103.23) and daylight (103.11) ones I see two others that could apply:
103.9(a):

No person may operate any ultralight vehicle in a manner that creates
a hazard to other persons or property.

This seems to be the part 103 equivalent of 91.13 (careless and reckless operations) and it's also written broadly. If you do go flying and something goes wrong, the FAA might argue that flying in marginal conditions was creating a hazard to other pilots or - if you lost control of the aircraft - to people on the ground. Whether or not that's plausible would depend heavily on the specific situation, of course.
103.21:

No person may operate an ultralight vehicle except by visual reference
with the surface.

In low light conditions with a lot of cloud and smoke around, it could be difficult maintaining visual reference.
So, if you're flying at noon, maintaining the required flight visibility, maintaining visual reference with the surface, staying out of TFRs, and not doing anything dangerous, your flight is probably legal.
But the important question here is &quot;is it safe?&quot;, not &quot;is it legal?&quot;.