Jasmine is evergreen.

It may come back from the roots, don't give up until it warms up. I think it is supposed to be hardier than the other confederate jasmines. I've had other evergreen (bay laurel) plants die to the roots and come back.

Your plant looks like Jasminum polyanthum. It really isn't hardy in the Upstate, but may come back from the roots. You might want to try Jasminum stephanense, which looks similar to polyanthum, yet is much hardier.

Madison is supposed to be Trachelospermum jasminoides.

I hope your plant makes it.

Dwayne--

Does Jasminum polyanthum have pink blooms? This is a white bloomer.

Jasminum polyanthum has pink buds that open white. If your flowers are pure white, it could possibly be Jasminum officinale (Poet's Jasmine). I haven't grown officinale, but it should be hardy here in the Upstate.