Contrary to popular belief people don't get sick actually from the cold weather or a change in the weather.
The most common reason people get sick when the weather turns cold is that the cold virus tends to hang around people during the cold winter months and during the winter months people are cooped up indoors more often which causes the cold viruses to be spread from person to person.
You can still catch a cold during the summer if the cold virus is there and you're indoors near other people who have the cold virus and you're inside places such as an office etc around those people.
I work in an office and I've caught the cold virus from a coworker who sits next to me at the computer so it's possible to catch the cold virus during the summer.