Although I cannot help regarding tellling you what the weather will be like in Japan at your specified arrivel date, I do wish to point out that the best thing you can do is layer your clothing. March in Japan shouldn't bee all too cold (although it might be relatively speaking). Look around on the net as there are always sites with weather trends, as do some guide books - the local library is fantastic for research, and if it isn't, check out your local Uni library.
Back to layering, it is better to wear several layers rather than one or two, as one can adjust clothing according to ones situation - which can change quickly upon, for example, entering/exiting stores or sunset. I suggest a comfy t-shirt, a top (preferably wool, merino if you don't like the itch) and a windproof jacket. The windproof jacket hould have a light padding - idealy removeable - so that if the wind picks up you'll be fine.
As for the cherry blossoms, AFAIK it is way too early, unless summer breaks way too early.