Basically, you will find Braunschweig to have similar weather conditions to the rest of this region - entirely unpredictable! For example, the photo displayed here was taken at the very start of Autumn here outside my loungeroom window and you are looking at sleet. Sleet, for goodness sake! However, in saying that Braunschweig just experienced its hottset October day in something like 30 years.
So in retrospect, my advice is to layer, layer, layer. I dont know about you but I would much prefer to be hot than cold.
Of course, keep in mind that what you have is an Australian giving advice about weather conditons in Germany. My city in Oz has over 300 days of sunshine per year so perhaps my view is slightly skewed :)
Rainy season: There is no special rainy season
Avg. Temp. in Spring: max.: 7 – 18°C ( 47 - 64°F ); min: 0 - 7°C ( 32 - 47°F )
Avg. Temp. in Summer: max.: 21 – 22°C ( 70 - 71°F ); min: 10 - 12°C ( 50 - 53°F )
Avg. Temp. in Autumn: max.: 6 – 18°C ( 43 - 64°F); min: 1 - 8°C ( 34 – 48°F )
Avg. Temp. in Winter: max.: 2 – 3°C ( 36 - 38°F); min: -1 - 0°C ( 30 - 32°F )