AI has happinesses bonuses over the human at all difficulty levels.
The main reason it's harder to win cultural victory with a larger empire is every city other than a puppet increases the cost of all cultural policies by 30%.
So, yes it is better with fewer cities.
But of course, if your four cities can take out your nearest neighbor whose built 8 cities and make them all puppets; then you get best of both worlds with 12 cities producing culture but only four cities on the cultural cost. And a couple of Cultural CS allies and your empire will produce a lot of social policies. (If your happiness isn't very high, the puppets will generally prioritize happy structures.) The downside of this is that it appears that other than a monument that puppets generally don't build additional culture buildings.
As to global happiness level penalties
At -1; you lose the science bonus policy (if you've chosen it) and growth reduced by 75%. Since growth is the main cause of becoming unhappy in the first place, doesn't really matter if you don't have that policy.
At -10; Empire is VERY UNHAPPY. major penalty on production and combat. Avoid this if at all possible.
At -20; Empire is IN REVOLT. in addition to the above penalties, rebel units spawn in your territory.
I actually briefly reached this as a result of a peace settlement ending the second german war giving me several cities on the same turn.
Got down to merely unhappy that same turn by:
1. Calling up an AI and asking how much gold he'd take for the least useful of Germany's cities. 85 gold. Deal. He promptly razed it.
2. Every non capital city in my core empire went from 1 specialist to 3. (I had the reduced unhappiness from specialist policy)
Only took a few turns to become happy even with the specialists sent back to the fields since several of my cities were already constructing Stadiums and the puppet cities started building Colosseums as well. (My core empire already had Colosseum's everywhere (& all luxuries) before the war started to maintain order; those were indeed mostly bought with cash.)
The guides I have read say it is easier to gain a culture victory with a small empire than a large one. I don't understand this because I thought more cities = more culture. Can anyone explain why this is?
Also just wondering how important happiness is. This game I've tried to keep over 0 happiness and have ended up with 6 cities while Japan next door has 11 (king difficulty). This is including a colosseum in most cities, so how come Japan can have so many cities but not be unhappy? And does it really matter if my citizens are unhappy because it only seems to affect food...