Elms can stay outdoors in a cold dark place protected from frost and winds. If you give it time to harden off it will be alright.
If you prefer to keeping it indoors a unheated room is perfect. It's normal they drop leaves this time a year. They also need to go dormant.
Growing them indoors and keeping them green all year long will eventually weaken the tree because it will cost too much energy.
In that case leaf dropping can have a lot of reasons like low humidity dry air in the room. Not enough ventilation, drafts, not enough light. sudden temperature changes, over or under watering, clumped up soil so the roots suffocate. You name it.
Best is to let them go dormant.