Hypothermia can set in when your core body temperature drops below 95 F degrees.
So if you're in the 40 F degree temperature water for too long then the 40 degree F water can cause hypothermia.
If you're just gonna be in the 40 F degree water for a short period of time you should not get hypothermia but if you do not get out of the 40 degree water within 30 minutes or so then it's possible to have hypothermia set in.
Hypothermia can be deadly if you do not get treatment and get warmed up.
I would highly recommend staying out of water when temperatures are cold and wait until it warms up.
You can also get hypothermia when the weather is just cold and not even freezing so be sure to bundle up properly when going out into cold weather.
The cold weather doesn't cause cold or flu viruses but you can get sick through hypothermia.