It is difficult to tell definitively at this point whether it's the mere exposure to cold that has triggered the vomiting, or if he's cooking an illness, since the fever has occurred for less than 48 hours. In the meantime you need to keep monitoring his temperature, and note any abnormal signs and symptoms like excessive persistent vomiting (notice the pattern, projectile vomiting is more worrisome), sleepiness, lethargy or inconsolable irritability/crying, any rashes, decreased appetite, decreased urine output; these signs should warn you that he's ill and prompt you to visit the doctor's office.