In general, the battle itself could be fought in a stormy condition, but in general at a more closed ranged form, due to lessened optical options. This in the end would have favoured the British, due to their in general larger calliber guns, which were at the same time more numereous as well. It would all come to a point, where the torpedo carrying vessels could have been brought into battle, as these could have inflicted serious harm to both sides.
In the OTL, German gunnery was more effective, as their optical systems were generally better, while the ranges to fight were a bit longer, benefitting these advances. In poor visibility, theis bonus would not likely have been there, so the two sides would have to face eachother at more equal terms in capabilities at least. Herre the numerical advantage would be crucial, as the German ships in general would be tougher to defeat, but face a possible outnumbering by 2 to 1. The heavier shot of the British could defeat the thick armor of the German ships at short ranges, while at the same time increasing the change of scoring hits, due to the shorter range.
Finally it would possibly come to a point where the increased safety on the German ships in ammunition handling after the earlier experiences, would come into play, as the shorter range would equally increase their own changes of scoring hits on British ships, which had been known to take a loop in safety messures in ammunition handling at the time. It could in theory be possible to see more ships blowing up, after hits on turrets, like in the OTL on four British ships (Indifatigable, Queen Mary, Invincible and Defence)