Well, since it's outside of Denver, open carrying is legal and protected by the state's preemption statute... however, Littleton is pretty close to Denver, so you might get some trouble from the more self-righteous of the city's inhabitants. Here's the relevant laws for you, in case you want to have something confirming the legality of open carrying around Littleton:
6-7-1: CONCEALING OR DISPLAYING IN THREATENING MANNER: (A)It shall be unlawful for any person to wear under his clothes, or concealed about his person, or to display in a threatening manner, any dangerous or deadly weapon, including, but not by way of limitation, any pistol, revolver, slingshot, cross knuckles or knuckles of lead, brass or other metal, or any bowie knife, dirk, dagger or any knife resembling a bowie knife, or any knife described in section 6-7-3 of this chapter, or any other dangerous or deadly weapon.
(B)Nothing in this section shall be construed to forbid any law enforcement officer from carrying or wearing, while on duty, such weapons as shall be necessary in the proper discharge of his duties, nor shall this section be construed so as to prevent the concealed carrying of any type of gun when unloaded and properly carried to or from any shooting range or gallery. (1971 Code, sec. 26.1)
6-7-9: FIREARMS PROHIBITED IN OR UPON PUBLIC FACILITIES: (A)The open carrying of firearms in or upon public facilities including, but not limited to: buildings, sites, areas, including municipally owned, operated, or leased buildings or properties; recreation facilities; and public parks, trails, or open space is unlawful when said facilities are posted with notification that the carrying of firearms is prohibited.
(B)Postings, including the appearance thereof, shall be approved by the city council.
(C)Nothing in this section shall be construed to forbid any law enforcement officer from carrying or wearing such weapons and firearms as shall be necessary in the proper discharge of his or her duties. (Ord. 18, Series of 2003)