No, if I've made a commitment to visit someone then I honour it regardless of the weather. Errands on the other hand..... well it would depend on what they were and how urgently they needed doing and whether I would be free to do them another day.
To be honest, given where I live, if I avoided doing things just because it's raining then I would never get anything done!
There's an old saying "There's no such thing as bad weather, only inappropriate clothing."
I HATE going out in the rain! However - I live in the tropics...where we have a wet season of approx. 4 months. During that time it sometimes rains continuously for weeks. So avoiding going out isn't possible. I have a bag for client meetings and it includes a change of shirt and a towel for "just in case" I get caught in a downpour. If I can avoid going out when it's raining I usually will - especially If I would have to take the kids. But more often than not it's just unavoidable.
But at night, prefer not, unless totally necessary.
Several weeks' ago, during really bad storm, I checked cost of a ticket I had for a Concert, & due ferocious weather, decided to stay home! I was happy with that decision as weather only got worse!
Also factored into that decision was the way others' drive on the road. I may not have an accident, but someone could hit me.
Discretion is the better part of valour, in this instance!