Thank you for your inquiry. In winter, all Begonias like sun and dislike sudden changes in temperature, but a 5 to 10-degree temperature drop at night will give you sturdier plants. Your plants may have a mildew problem, caused by high humidity and cold temperatures. Or, it could be botrytis, a fungus that spreads rapidly when plants live with high humidity, poor light and not enough ventilation (similar to mildew); from that they may not recover. Damaged leaves should be pinched off.

There are several types of begonias with individual care needs to keep them healthy. 

Fibrous types include: Wax begonia which need a sunny, warm position, and Angel wing begonias, another fibrous type, must not be kept constantly moist or leaves will fall. Use clay pots and guard against overwatering. Let dry between thorough waterings.

Rhizomatous type: these plants hold lots of moisture. The soil should not be kept constantly moist. A slight drying on the surface soil between waterings will maintain healthy roots.

Rex type: Rex Begonia’s dormancy period must be watched for. When the plant is dormant, water sparingly.

Tuberous types: need to be kept moist, but not soggy, at all times, along with filtered sun, east or west window protected from hot noon sun in summer. The temperature needs to be under 75 degrees during summer or the flowers will be short and dried.

Hope this is helpful.

Courtesy of NYBG Plant Information