Ok. At this point I will assume that it’s going into dormancy. In that case should I put it outside even though it can get very cold where I am?
Probably not. My elm has had time to adapt. It has already lost all its leaves and will get through winter just fine (assuming it will not get extremely cold).
Best thing would probably be to find a cool space, like an unheated room or shed.
What are the light and watering requirements during dormancy?
I do not water at all in this period. They get enough rain - probably too much, but I do not have a sheltered space (I should build one...).
If I could keep it out of the rain, I would water sparsely. The soil will not dry quickly outside so I would just have to make sure it doesn't dry out.
When does then dormancy period end?
When the buds start leafing out, somewhere beginning of spring, depends on how much light it gets and/or the temperature (not sure which of the two triggers dormancy in chinese elms - or if it's both. You'll need to look that up).