Here's the quote :
The context is "three frogs are taking hands and are ready to go for a walk".
At first I thought こう here meant "let's go" but that would be いこう right?
The other possibility could be the adverb こう (more often そう) in which case it'd mean
"they took each other's hands and like that [they went for a walk]" implicitly referring to the verb in the previous sentence.
I've never seen this grammatical construct before.
Therefore I am not sure what's the precise meaning here, plus it's quite an old book I guess so It could also be an expression that is not used anymore. What do you think?