Has holding hands gone out of fashion? I offer my wife my arm on more formal occasions; nice evening out, the theater, weddings, coat-and-tie affairs and so on. Daily out and about; stores, movies and so on, we simply hold hands.
It's generally uncomfortable for me to hold hands unless the young Lady is the exact right height and arm length. It's more natural and comfortable for me to give her my arm. The exception is that at times here in the old south, it can be a little too hot for that close of contact, in which case instead of holding hands or giving her my arm, I do that hand pressed gently against the small of her back thing as we walk together.