No, it doesn't always change the meaning. Logic comes into it, apart from anything else. No one would think that you like to read a book and watch a movie at the same time, regardless of the day of the week!
The thing with your original context was that "go and do something" (which is effectively what "go for a walk and visit" suggests) is used, in BrE at least, to express two things in one action.
I want to go and get a takeaway tonight.
He decided to go and visit his mum.
We want to go and take photos of the sunset this evening.
In all three sentences, "go and" might well be included by a native speaker even though the actual meaning of all three could be expressed without those two words.