Depends on what species it is. You can try searching for the species name or common name aswell as 'food plants' and you will find people talking about which plants have been successfully used with your species. Many of these food plants can be sprouted from seed in little pots cups or trays, indoors under lights, to produce a few leaves each to feed your bugs with. If you plant many you will have enough for the winter. Its also possible to use dried leaves, for some species, if you mist them but I believe that requires carefully drying fresh green leavesthey are still in season.
Heres a link for you with regard to winter feeding, it explains the drying method and which species have thrived on them, also describes how to grow acorns for feeding most species:
http://www.phasmatodea.com/web/guest/forum/-/message_boards/message/452252;_19_threadView=flat
Thats also a good placeto learn more about your stick insect is the Phasmid Study Group :
http://phasmidstudygroup.org/