No, most(?) deciduous trees are hardwoods.
Hardwood
Specifically, a softwood is wood milled from a deciduous tree.
Larch is a softwood and a deciduous conifer.
Aspen , being a deciduous tree, provides a hardwood.
To my knowledge, any deciduous tree ( A tree that loses it's leaves in the winter) is considered a hardwood. Even the Tulip Poplar tree that is most often mistaken for a softwood, is a hardwood tree.
Hardwood. All deciduous (leaf bearing) trees are hardwoods.
Hickory trees are deciduous but they do live in coniferous forests.
A Deciduous tree
The terms coniferous and deciduous refer to trees, rather than particular kinds of forests. Forests described as coniferous or deciduous are those containing primarily those kinds of trees. Coniferous trees are trees which don't change over the seasons, like evergreens and other pine trees.
A spruce tree is a coniferous evergreen (pine needles and cones) and most maple trees are deciduous (leaves fall off).
As coniferous wood is softwood it would be inclined, given the same conditions, to decay faster.
Answerdeciduous trees are considered "hard wood" trees, and coniferous trees are "soft", even though some deciduous trees are soft and some coniferous trees are hard. but to answer your question, yes ash is a deciduous wood but it is soft and light. AnswerAsh is a hardwood.