Carhartt Women's Hamilton Plaid Loose Fit Hooded Shirt Jac

Is this a women's shirt or a jacket?

Both. It's cut like a flannel shirt with a snap front, but it's longer and roomier than a standard shirt, so it works as your outer layer on cool days or over a tee when it warms up.

Is it warm enough on its own?

It's an unlined brushed flannel with a hood — good for cool days on its own and easy to layer under a coat when it gets cold. If you want insulation, look at the Highland Shirt Jac instead.