Anna is right. It's a little old-fashioned to use 'but for' in place of 'if it weren't for', but it's still very common, especially in the north of England. "I would take my coat off but for the wind." "I would take my coat off if it weren't for the wind." I would like to take my coat off, but I'm not going to, because it's windy. "I'd travel around the world but for the cost." "I'd travel around the world if it weren't for the cost." I would like to travel around the world, but I won't, because of how much it would cost.

This is an old-fashioned or poetic way to say, "I would go for a walk if it were not for the rain." You could also say, "I would go for a walk if it weren't raining."

If it's phased exactly like that it may mean that you would go for a walk to enjoy the rain. Say if it has been hot for weeks without rain and it suddenly rains. People might take a walk in the rain to cool down during the hot weather.