marcia,

if you read the Nature Article, the mechanism for generating an ice age on Earth comes from the disequilibrium atmospheric chemistry unique to Earth. Gamma rays fragment N2 and O2 molecules, which recombine randomly into assorted NOx, which is relatively dark and transmits light poorly. Thus solar radiation is intercepted at altitude and warms the upper atmosphere, whilst the ground cools - instant ice age.

Eventually, the NOx gets washed out as acid rain, and reconverted by slow abiotic processes nitrates and then biotically back to N2 and O2, and the world recovers, but the ice age may take some time to dissipate due to its self-reinforcement by high albedo (reflectivity).

On Mars and Venus, the atmosphere is >95% CO2. Gamma-radiation will lead to fragmentation and recombination to COx (CO and CO2, which are both transparent), plus O2 and possible organic carbon (soot). The small amounts of soot that survive re-oxidation by O2 may lead to a slight dimming of the sun, but it is a very minor effect in comparison to Earth.

On Mars, the effect would be like a global dust storm, which has similar upper atmosphere heating and surface cooling effects. These occur every few Martian years.

On Venus, the higher temperature and rapidly-circulating atmosphere would rapidly destroy any soot, so the effect would probably be trivial.

On the gas giants, not much will happen, since their atmospheres are a cycle of molecular breakdown and recombination anyway (although the cloud levels would be upset).

Titan's atmosphere is already a thick smog of N2 + CH4 + trace organics including HCN, CO2, C2H4, H2O. Blasting this mixture will result in more of the same - i.e. no change.

Europa's icy surface would be radiolytically split to O2 + H2 + OH, which would recombine rapidly in a flaming corona to produce H2O again. Some of this would be lost to space, but some would fall back as snow.

So, in conclusion, Earth is probably unique...