I don't want to cuddle with my wife at night because I want to read
Would you prefer reading to cuddling with your wife normally.
I like to read at night. That is my time.
Well hopefully your partner understands that you need your own time as well. This does not sound unrealistic.
I really can't understand why she needs to be cuddled. When I'm reading I'm content, I don't want to cuddle at all.
I think if you just explain to her that you need some private time to read, then she will respect your wishes. Then you can cuddle her afterwards.