"Hand in hand" is idiomatic (in both English and Swedish, apparently" for "holding hands". If I was expressing the idea in English I'd probably say "They came along, hand in hand", but I suspect "walking" is in there because it's gående, not åkande. ("De kom åkande hand i hand" sounds dangerous, if nothing else).
Can you say 'de kommer gående hand i hand'? Or would that just be 'de går hand i hand'?