After leaving Law Enforcement in Los Angeles, I lived in this world for a little while so my educated guess is that Arnold likely has a private security detail as a lot of famous Hollywood types do.
Private security details are usually former police officers or members of the military...so they often look the part (broad shoulders, dark suit, crew cut, etc). Depending on who they are protecting and the circumstances surrounding them at the time, their attitude can be anything from chill and laid back just part of the crowd to extremely visible and highly aggressive. Ironically, the big scariest looking bodyguards are usually patient and pretty nice, its the average height, slim, nothing special looking but former Special Ops guys that will light you up.
When Arnold was Governor of CA, he had security from a Division of the California Highway Patrol called DPS (Dignitary Protection Section).
www.chp.ca.gov
The Secret Service is part of the Federal Government and protects the President, Vice President, and some of their family members. In certain circumstances the Speaker of the House and others in line for succession, and visiting foreign dignitaries also have Secret Service protection. Sometimes other federal officials will receive it upon request if there is reason to believe they are targeted for harm (such as a Senator, Congressmen, or Federal Judge who may have received a threat).
I know it may seem counterintuitive for a large and athletic man like Arnold to hire security protection, when he was in his prime, but it is not unusual at all. Once someone achieves enough fame most will seek out either full time protective details or at least security for specific circumstances and occasions. Even most boxers and UFC champions will have a detail because what they are protecting against is not some random dude who wants to have sparring match.
They are paying to be protected from stalkers, people with serious mental problems, fame seekers, and especially people looking to start something hoping it will result in a law suit in their favor. (If Arnold's bodyguard slaps and pushes you..... it's not going to have the same legal / financial risks as Arnold slapping and pushing you).
If they contract with some of the higher echelon companies their bodyguards are licensed to concealed carry with reciprocity between most states and in many cases in foreign countries. It is now becoming very popular for many of them to also deploy personal protection K9 Teams.
Anyhow...probably more than anyone cares to know, but thought I'd offer it up.