Leave the jasmine for a few days up to a week after a freeze before pruning. Plants may look damaged after a freeze, but will return to their former states after a couple of days.
Check the dampness of the soil post-freeze, and water if it feels too dry. Do not over-water, but gently pour water over frozen foliage to melt the frost. Perform this action early in the day so the jasmine leaves have time to dry out before nightfall. Keep your jasmine watered going into a freeze, if possible, to protect it. The leaves should be dry; however, you can water the roots to keep them from becoming dehydrated.
Remove any plant tissue after a few days or a week's time that appears mushy, slimy, foul-smelling or oozy. Trim back any parts of the jasmine that are dead or damaged beyond repair. Because downy jasmine is a vining plant, perform any necessary maintenance pruning to train the jasmine in the desired direction. Pinch off new growth if you want to encourage bushier growth and optimal blooming.