I do have some personal experience with privets, all of mine (I have 6) overwinter outside. Last winter, they were fine in temperatures as low as -15C. I bury the pots into garden soil so that the level of growing medium in the pots is a little above that of the garden soil (for good drainage), then mulch goes over the bonsai's root ball. It is best to bury the pot in a spot that is protected from wind. They are not deciduous, so shouldn't normally lose their leaves. If you look at the nodes on smaller branches, you may be able to see when the new leaves are starting.
There is a page under species guides here on Bonsai Empire for Ligustrum, that is the botanical name for the privet.
A general note for trees that need a little extra help, there is a product called Super Thrive that many bonsai people use to soak root balls in. It is kind of like feeding your tree some vitamins. I keep some mixed in a spray bottle, and mist the root ball of a tree that isn't doing so well, or a tree that I've just transplanted.
