What does "in the saddle" mean?
Solution 1:
Typically, in the saddle means:
- seated on a saddle
- in a position of control
The article you quoted goes on,
I have to laugh whenever I hear Republicans ranting that Barack Obama is a “liberal” or a “socialist” or a communist. Are you kidding me? Obama is Bush 44. He’s a bit more like the old man than the younger one. But look at who’s still running the economy: Bernanke. Geithner. Summers. Goldman Sachs. J.P. Morgan Chase. We’ve had the same establishment in charge since at least 1987, when Paul Volcker stood down as Fed chairman. Change? What “change”?
So this is saying that the ancient regime is really "in the saddle", or in control. The names the article refers to--Bernanke, Geithner, Summers--are all men who have ostensibly been in control of the economy since the 1980s. So, even though Republicans say Obama is a "communist" or "socialist", in reality nothing has changed (in the author's opinion) because the same men are in power.
Solution 2:
As @simchona says, in the saddle means in a position of control.
It's a simple metaphor - particularly appropriate for Americans, taking into account the history of horseriding/cowboys/etc. There's also holding the reins - much the same metaphor and meaning.
A related metaphor based on cars rather than horses is in the driving seat (British) or in the driver's seat (American), which has rising usage whereas the equine ones are falling.