We at Discover Tuscany personally don't support hunting as a sport here in Tuscany but understand that hunting is necessary for population control, as in the case of wild boars where the end product turns out quite tasty ;-)
But because we don't in any way follow this area, I admit I am completely ignorant on the seasons for hunting... I believe it starts in September and goes on until January. March I think as spring nears is likely off the season as any wild animals might be ready to birth their young ones?? You'd definitely need to purchase a license but, again, I am not sure of details.
In any case, March would be perfect for other outdoor activities such as cycling, hiking or just enjoying the charming medieval villages and Renaissance treasures that Tuscany has to offer If you have any other doubts, do post and we'll try to answer as best we can.