If it were mine, I'd keep it inside in a bright sunny location for the winter and then get it outside in the spring ASAP.
If you plunk it outside now and it's still in leaf, you could be killing it. Dormancy is NOT induced by simple exposure to colder temps. It is a process that begins in mid-summer. In warmer climates, Chinese elm is almost evergreen and can hang onto leaves all year. Some varieties are more cold hardy than others. If the tree isn't dormant now it won't have time to prepare itself, or hasn't built up enough resistance, for immediate cold (below freezing) temps.
I tend not to let warm snaps make me believe the entire winter (or even the next week) is going to be warm. A plunge into the deep freeze is never far off in your location...