grammar - Function of the sentence final particle こと in this sentence

I am wondering what is the correct way to interpret the こと in this sentence:

どこかへお花見に行きませんこと。

It is an example sentence found in the book "All About Particles" (page 120). It's described as being basically an alternative way to entice/invite someone to do something together. If that's true, how does　こと change the meaning and feeling of the sentence, especially when compared to:

どこかへお花見に行きませんか。

どこかへお花見に行きましょう。