"I am proud to be a member of the party of Abraham Lincoln, I am proud to be a member of the party of Ronald Reagan." -
Arnold Schwarzenegger, 2012
Yeah, he still makes plenty of speeches and does a bit of fundraising and endorsing of candidates.
The only California governor to ever win a recall election sees the same atmosphere today that existed in 2003.
www.politico.com
Politically he doesn't fit perfectly into either party, he tends to be fairly moderate and centrist, and leans more right on fiscal issues and more left on environmental issues. He had a lot of ideas for California and but was basically unable to actually do anything, totally hamstrung by the rest of the state's politicians and their voting system.
He hasn't done much besides endorse candidates since being governor of Cali because there's not much else he can do, as a naturalized citizen he's not eligible for higher office and he served out his term limits in California.