But does it really? I've just started the second volume of the book and the rural peoples are frequently described as ignorant, resistant to change, and generally not equipped to handle even the most basic of tasks that will better their futures. In that sense, ignorance is bliss as the peasant class is both unwilling and incapable of understanding urban ideologies exemplified through Levin's painstakingly slow reforms.
Vladimir Lenin seems to agree with this, at least in part. The Lenin Anthology edited by Robert Tucker includes Lenin's 'The Tasks of the Russian Social Democrats.' Lenin encourages the educated urban proletariat to educate the rural peasants as they were poorly educated and thus easily exploited by the land owners.
I agree that Tolstoy tells of rural lands of gaiety, but only in the sense of extreme ignorance on the part of the peasants. The passage where Levin goes to work the fields with the peasants comes to mind as the most obvious example (the happiness from hard labor, the songs among the farmers, etc)
I can't give any sources on the noble class besides the general assumption from the above that rural life was a place of refuge for the elites as it was away from the intrigue of St Petersburg and Moscow and sustained on the backs of cheap and ignorant labor.
Not a history guy, but a literature one. One thing that should be kept in mind with Anna Karenina is that the social dichotomy you speak of was put there as a commentary on the social upheaval of the time, so it is likely exaggerated, but not wholly unrealistic. He is partially showing this conflict between the old Russian paternal patriarchy and the liberal, "libre panseur," ideas coming in from the West so he can in the end say that western ideas won't really work in Russia.
He is generally regarded as a realist in terms of setting so he uses real historical issues of the time as backdrop, like the Emancipation Reform of 1861 and the development of the Zemstvo. Lenin may have been able to grab on to many themes inside the novel as even though Levin tries to help the lower class, he begins to realize it cannot be achieved using western ideology--thus the need for new, non-western ideas.
So basically, from a literary stand point Tolstoy IS reflecting the times he writes about, but from a historical one it must be remembered that this is largely commentary.