It doesn't look like Schwarzenegger is in the running to be the next governor of California.   However, this article by a Democratic strategy consultant in the National Review is pretty eye-opening w.r.t. the Terminator's politics:

Schwarzenegger's politics also changed as he aged. A Reagan Republican and a staunch conservative in the '80s, he moderated his politics in the last decade. Schwarzenegger says he is pro-choice, supports gay rights, and endorses "reasonable" gun controls and environmental regulation.

During the Clinton impeachment drama, Schwarzenegger said he was "embarrassed" by Ken Starr's investigation of the president's private life. While his fellow national Republicans appear to be tilting right, he's followed the recent leftward drift of California politics. He has ended up being a lot closer to Clinton than Newt Gingrich.

As someone who's never held office, he's free to create an ideological profile. Schwarzenegger seems a fiscal conservative and social liberal, very much in the mainstream of California politics. Dan Weintraub of the Sacramento Bee calls him a "pragmatic libertarian," who believes in both the merit principle and "providing the opportunity for every child to fulfill his dreams."

Surprisingly sophisticated for someone we'd otherwise file away as a meat-head, eh?   I remember seeing another report here in the Financial Times where Arnold described his economic policy:

His economic views were defined early: "I am more comfortable with an Adam Smith philosophy than with Keynesian theory." (Not a line you expect to hear from Conan the Barbarian. Or then again...) In 1980, the year he became an American citizen, he bombarded friends with tapes of Milton Friedman's television series Free to Choose. Arnold himself felt free to speculate in property and real estate with bewildering success, or beginner's luck, during the 1970s.