It is a bit of a dilemma and I think the answer (at least partly) depends on how it has been treated up to now.
Chinese elm is a sort of in-between tree. Temperate trees (evergreens like juniper and deciduous like maple, oak) have to be outdoors all the time. Tropical evergreens like ficus make good indoor trees. Chinese elm is a subtropical. Some people do keep them indoors. If yours is used to being indoors, I wouldn't put it out now, if it is already cold and snowy where you are. To winter over outside, they need to go through the autumn, to gradually toughen themselves for winter. After the weather warms up next spring, you can gradually transition it to outdoors.
Chinese Elm trees are very flexible about their environment. If adapted
properly, they can be grown indoors year-round. If hardened off to
the cold gradually, they can drop their leaves in the fall and be
considered deciduous trees, so you have a few options. However, it is
important to find out how your Elm has been growing recently. Some
Elms come from southern China, and have never experienced cold
conditions. It would be dangerous to keep these Elms too cold the
first year or two. Other Elms have gone to freezing and dropped their
leaves for many years; as a result, these Elms may not be too happy
indoors for the first year or two. If you can not determine where your
Elm has been, then keep it outside for the summer and bring it inside
for the winter. You can bring it in when the temperatures are around
50Â°F. If kept indoors for the winter, a cooler location is preferable
(50Â°Fâ€“65Â°F). Chinese Elms may drop some leaves in the winter due
to the natural decrease in light. This is normal.