I think we have two issues of disagreement. The first is that the Woodhouses are unacquainted with the Coles and the second is that I suggested Emma snubbed the Coles. (:D)

IMO Emma has maintained a cool distance between herself and the inferior Cole and Cox families. This is her prerogative as a lady and of her higher status but her fleeting thought that William Cox (a lawyer) might do for Harriet (16) evidences that although she believes him to be socially inferior to herself she does not feel he is beneath her acquaintance unlike poor Mr. Martin who is only a gentleman farmer. The Coles appear to outrank the Cox family by fortune at least so it stands to reason they are not beneath her acquaintance either. I think there is evidence of acquaintance (not socializing prior to the Cole’s party) with both families. IMO Emma is acquainted and has exchanged civilities with them when it could not be escaped—perhaps after church, just in town or at the Bates apartment:

She had had many a hint from Mr. Knightley and some from her own heart, as to her deficiency -- but none were equal to counteract the persuasion of its being very disagreeable, -- a waste of time -- tiresome women [the Bates] -- and all the horror of being in danger of falling in with the second rate and third rate of Highbury, who were calling on them for ever, and therefore she seldom went near them. (19)

A prior acquaintance with the Coles is evidenced by Emma’s assumption for many weeks they would send an encroaching invitation (25) because I agree they would not take the liberty if they had not at least exchanged some civilities in the past. Her opinion they are “very good sort of people -- friendly, liberal, and unpretending” (25) seems one based on personal experience. Mr. Woodhouse laments “it would be much better if they would come in one afternoon next summer, and take their tea with us” (25) which I cannot imagine he would suggest if they were strangers.

I think either Emma has some level of acquaintance with the Cox family as well or she sat through a dinner with a man who has never been introduced to her and that seems unlikely to me. The “the male part of Mr. Cox's family, the lawyer of Highbury” (26) was of the Cole’s dinner party. Emma’s judgments William Cox might be right for Harriet but felt “Oh! no, I could not endure William Cox -- a pert young lawyer” (16) and the “less worthy [Cox] females” (26) looked “Just as they always do -- very vulgar” (27) also seem to be the result of personal experience.

I never meant to suggest Emma snubbed the Coles what I said is she was less gracious towards them than Mr. Weston and Mr. Knightley. I don’t consider a snub and less gracious to be the same thing. A snub is “an affront, slight, or rebuff” (dictionary.com) and gracious is to be “indulgent or beneficent in a pleasantly condescending way, especially to inferiors” (dictionary.com). I feel Emma was less indulgent, beneficent and condescending to the Coles than Mr. Weston and Mr. Knightly. Perhaps a better description is Emma’s “manners, though well-bred, were not inviting” (P&P, 4) towards the Coles and IMO that would signal to them an invitation to their party would be unwelcome. IMO the Coles do not have to be snubbed by Emma to understand she has no wish of familiarity.

Emma’s reflections on her performance at the Cole’s party are hilarious and I think do her no credit. I see a great deal of self aggrandizing without gratitude to the Coles for the pleasant evening they provided. Her enjoyment “in the splendour of popularity” that she “must have delighted the Coles” and “left a name behind her that would not soon die away” (27) reminds me a great deal of something Sir Walter in Persuasion would feel. I am glad Emma sees the Coles as worthy people now but I am discouraged to know she only gave them a chance because she was envious of all her friends gathering for an amusement without her. Having attended the Cole’s party I wonder if Emma will reciprocate with an invitation to Hartfield? Would that not be the right thing to do?