http://www.scientificamerican.com/article.cfm?id=impure-as-the-driven-snow

Zender, physicist Mark Flanner and other colleagues built a model to examine how soot impacts temperature in the Arctic and Antarctic regions. Temperatures in the northern polar region have already risen by 1.6 degrees Celsius (2.88 degrees Fahrenheit) since the dawn of the Industrial Revolution. The researchers incorporated information on soot produced by burning fossil fuels, wood and other biofuels, along with that naturally produced by forest fires and then checked their model predictions against global measurements of soot levels in polar snow from Sweden to Alaska to Russia and in Antarctica as well as in nonpolar areas such as the Tibetan Plateau.

Unfortunately, the soot problem extends beyond snow, he says, noting that similar studies are needed to assess how the smut affects the melting of sea ice. That meltdown may be the impetus for an accelerating doom as it opens up shipping lanes previously blocked by ice in the Arctic Sea. “Those ships are great emitters of soot,” Zender points out, adding that, “putting a locally heavy source in the Arctic in the early spring,” is virtually guaranteed “to polish off the summer sea ice.”

Dr. Hansen confirmed this in 2003 :

Plausible estimates for the effect of soot on snow and ice albedos
(1.5% in the Arctic and 3% in Northern Hemisphere land areas)
yield a climate forcing of
0.3 W
m2 in the Northern Hemisphere.
The ‘‘efficacy’’ of this forcing is
2, i.e., for a given forcing it is twice
as effective as CO2 in altering global surface air temperature. This
indirect soot forcing may have contributed to global warming of
the past century, including the trend toward early springs in the
Northern Hemisphere, thinning Arctic sea ice, and melting land ice
and permafrost.

The soot effect on snow albedo may be responsible for
a quarter of observed global warming.

The chart below shows Hansen’s calculations of the temperature effect of soot by season and latitude. He shows 1-2C warming across the Arctic due to soot.

In other words, reducing CO2 emissions (if it were possible) would have very little   effect on Arctic ice, because they aren’t the primary cause of the problem.