There is no need to wean her!! Continue breastfeeding as long as you like. Your daughter will not get sick from it being cold at night. She will only get sick if she is exposed to some type of virus/bacteria. Breastfeeding is the best protection due to all the antibodies that are present in it. The change in temperature does not cause someone to get ill. Sweating is the body's natural response to regulating their temperature. Some kids sweat more than others.
Hope this helps.
L. Kandell, MS, RD, IBCLC
Registered Dietitian/Pediatric Specialist
International Board Certified Lactation Consultant
AFFILIATED NUTRITION CONSULTANTS, LLC
Scottsdale, AZ 85258
Mother of two - 8 yr old daughter, 5 1/2 yr old son