What they often can't handle is exposure to cold drafts. Placing an indoor plant, especially a tropical or blooming plant, near a frequently opened door to the outside or too close to a window with limited insulation will have the same effect as leaving the plant unprotected outside. You will probably first notice leaves dropping and the plant may look like it needs water, when actually it needs warmth. Repeated or prolonged exposure to cold temperatures will kill a houseplant.
Light is limited during the winter months and it's tempting to want to inch your plant closer and closer to the window. But plants slow down their growth processes during winter and a bright light in the center of the room should be sufficient. There the plant will be warm and content until it moves out of its semi-dormancy, in spring.