Rain has been known to affect WiFi internet so it is possible for internet to get slower when it rains especially if you use WiFi.
Even if you have a wired internet connection the internet speed can sometimes be affected due to rain getting into wired connections.
On my DSL internet line in the box outside it was getting wet and causing a short in the wires which then caused my internet speed to slow down.
Sometimes the internet would cut in and out and I couldn't figure out what was causing the issue.
Turns out the cause was the wires getting wet and corroded and the technician came out an installed new wires, a new telephone box and made sure it was sealed properly.
After he did all that the internet speed stayed the same and it quit dropping out when it rained.
Rain can also get into other wired connections that lead from your house out to the internet providers equipment.