Cut back the entire jasmine plant to within 6 inches of the base. Cut off all the stems just above a set of leaf nodes. Use freshly cleaned pruning shears since dirty shears can transmit disease to the plant.
Water the jasmine thoroughly after pruning it back. Run a garden hose on low volume near the base of the plant for five to 10 minutes, or until the soil is moistened at a depth of 4 inches.
Spread a 6-inch-thick layer of pine-needle mulch over the jasmine plant to protect the roots from frost damage. Spread the mulch in a 12-inch radius around the plant to further insulate the soil.
Lay a blanket over the mulch when the weather service predicts a hard freeze. Remove the blanket the following morning to keep the jasmine plant from suffocating.
Remove the mulch in spring once all danger of frost has passed. Watch for renewed growth three weeks after daytime temperatures consistently remain above 65 F. Resume your normal care routine once the new growth emerges.