From what I've seen, it's really really hard.
I've played 3 whole games now, 2 small maps, 1 std.
1st go Prince, other goes Emperor. Victories by Domination the 1st two goes, then science on the std map.
I really really tried for a culture victory on the 3rd go, I was playing on archapelago and limited myself to 3 cities (4 later as I needed more production power and oil/coal that it provided).
I built pretty most wonders and had over 10 in my capital, went for all cultrual buildings and policies. In the end I needed another 15 policies, so was absolutely miles away from victory!
I even had 3 city states giving me a whole bunch of culture, made bigger by playing as Siam.
It looks like you need to limit it to 1-2 cities, but I'm not sure what else I could have done and would have been beaten to a science loss if not for the oil which let me take over an enemies capital as he was building his spaceship ahead of me.