Im blaming my mother-in-law for getting my baby sick ?

Ok my mother in law had been sick for a couple of days. Then on Friday she got worse and had a real bad cold. Now all of a sudden my baby got really sick yesterday she started off sneezing, then coughing really bad, she is also really congested and has a stuffy nose. She wasn't able to sleep all night. I gave her a nebulizeer treatment and rubbed baby vicks on her it kind of calmed her down. So my mother in law lives with me and woke up in the morning to tell me that the baby is sick because I took her outside in the cold even though she was all covered up with a blanket. So is that true that a baby gets sick from me taking her outside too often. Oh and by the way my brother in law is also sick.my baby is 29 months.