So far temperatures in Siberia haven't been as hot anymore as before the fire season started in earnest. I wonder if that's just a coincidence, due to the weather, or if the smoke is causing a temperature drop. It would be logical that if we had high temperatures because of clean air, that dirty air from all that smoke would lower them again. If they stay lower than they have been pre-fire season, this could be another negative feedback loop, no? Not that these fires will do any good long term, or for the melting season as that black carbon gets dropped on the ice, but what do you think? Is smoke from more extreme fire seasons a negative feedback loop?
It is without any doubt negative feedback short-term - "then and there". Cleaner air means hotter surface, while air with more particulates of any sort (smoke, aerosols of all kinds, clouds, what have you) means cooler (than otherwise expected) surface, "then and there".
That said, forest fires in Arctic itself cause more than just "make lots of air dirty again". Those throw up serious amounts of GHGs, too - i mean high local concentrations of those gases. Something which is not done by "usual amounts of aerosols" travelling to the Arctic from NH's industrial belt: those come with GHGs already dilluted down to pretty background GHG levels. And, as you mentioned, soot on ice is another, if "a bit delayed", effect.
And then there are of course many other differencies between "industrial aerosols" and smoke from forest fires, as well, which are presumably not as strong as above ones but still significant enough to worth a mention at times. Like, for example, lots more black soot in forest smoke than in industrial outputs due to way more efficient (than just burning some wood in open air) combustion of fuels which industries perform, and lack of any soot-filtering equipment over forest fires (obviously). Black soot absorbs way better than most other aerosols, resulting in generally more heat trapped within troposphere which then has further (mostly unpleasant) effects for sea ice further into melt season. Etc.