overwintering Jasmine

in Plants
Greeting community! I have a now quite large Jasmine that has been going bonkers in the conservatory all summer, putting on loads of growth from a very tiny plant. Now that it's getting colder in there and the heating is down to about 11o, to give the plants a chance to go a bit dormant, my Jasmine is looking a though it's starved of water, but its soil is "just"moist. Do I cut it back vigorously, and put it in the greenhouse to let it start again in early spring? or if I cut it back will I kill it?....... thoughts please!????
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it's a Commom Jasmine Officinale which was given as a very small house plant. It's now grown up a large support and is very full! but in places it's going dead looking and crispy and looks unhappy although it is slightly damp soil. it has been kept in the conservatory all summer, going really great with masses of lovely fragrant flowers.