The climate in Pistoia is what you can expect anywhere in Italy: hot summers and cold winters, but not too cold.
In summer temperatures can go as high as 40°C and, due to humidity being sometimes very high, the perceived temperature is extremely high. Fortunately this doesn’t happen everyday in summer.
Periods of very high temperatures usually don’t go over two or three weeks spread over the entire summer. Winters, specially due to the fact that the city is bordered by the Apennine Mountains, are usually cold and rainy.
Temperatures can reach -10°C, but the average during winter is about 1-2°C.
During Spring and Autumn temperatures vary a lot, there can be very hot days in Spring and Autumn as well as rather cold ones in Autumn, but this is nothing that should worry the tourist.
Bring some light jacket or tshirts just in case you bump into one of these odd days.