As historian Glen Fryxell puts it, "it is a reminder of how Americans see themselves, independent, free and capable".The font used in the logo is probably custom, based on many similar semi-script serif typefaces that existed at the time.
Winchester
Winchester has a similar logo, a horse mounted cowboy at full gallop, trusty Winchester rifle in his hands.
Although reminiscent and perhaps inspired by the works of Frederic Remington (again, no relation to the gun company), the logo was actually created in 1919 by artist Phillip R. Goodwin. The Winchester stylized serif font was created earlier, maybe as early as 1903.
Smith & Wesson
The famous Smith & Wesson logo is perhaps one of the most recognized brands in the World. It was first trademarked in April of 1913 as just the S ampersand and W. The circle and two 4-pointed stars came later. It was originally designed by engraver Louis Nimschke circa 1876.
The font used in the logo is a heavy version of the Clearface font, created in 1907 by American Type Founders, designed by father and son team of Morris and Linn Benton.
Beretta
Beretta holds the distinction of being the oldest gun maker in the World, having been founded in 1526. The current logo is much newer of course.
The modern logo was adopted in 1962 and is known as "the arrows".
It was inspired by a poem by Italian poet Gabriele d'Annunzio (1863-1938). Entitled "Dare in Brocca" which Beretta claims to translate as "hit the target", although the translation in both Italian and Latin are a bit different.
Mossberg
Officially known as O.F. Mossberg & Sons, the company was founded in 1919 by Swedish immigrant Oscar Frederick Mossberg and his two sons.
The logo is without question inspired by the Swedish national flag, which makes sense as Oscar was born in Sweden. The three crowns are also a national symbol of Sweden.
The font is called ITC Benguiat and was created in 1977 by Ed Benguiat and release by International Typeface Corporation. It was influenced by earlier Art Nouveau typefaces. Most likely Mossberg paid a license fee to use the font commercially.
Sig Sauer
Sig Sauer, if you didn't already know was a merger between SIG Arms of Switzerland and J.P. Sauer & Sohns of Germany. The merger occurred in 1976.
The font used is believed to be the Entrusco font. Created in the early 1920s by an Italian typographer company called Niebolo. The company began using this logo in 2007 when they changed their name from Sig Arms to Sig Sauer.
Colt
While the modern logo is simply the name, the company still imprints their firearms with the famous rampant horse image so I will include both here.
The rampant horse goes back to the founding of the company in 1857. It is not known who created the logo. According to the Connecticut State Library, the rampant horse harkens back to the "days before firearms, when crusaders went into battle on horseback armed with spears, one very intelligent horse, seeing that his rider was about to be pierced by the enemy's spear, reared on his hind legs, grasped the spear in its mouth, struck out with one hoof and broke the spear: This is emblematic of the Colt, always coming to the defense of its master."
The stylized Colt font has a custom capital C which is meant to look like a horseshoe, the rest of the font is simply a bold, block sans serif font.
Remington
Remington was founded in 1816 and is considered America's oldest gun maker, although lapses in production may have taken that title away.
The logo is a serif font, probably custom, although there are others similar, so it is possible that it was type face used at the time. It is believed to have been adopted in the mid 1920s, as it was 1926 when the logo began appearing on everything from gun boxes to knives, camping gear and other outdoor apparel. It was later, although I don't know when, that the specific shade of forest green was adopted as the company color.
Springfield Armory
This one has some "murkiness" as well. The modern company that goes by the name Springfield Armory Inc. was incorporated in 1974. The company has absolutely no connection to the actual Springfield Armory which was founded in 1777 by George Washington.
The crossed cannons and flaming bomb were not created by the owners of the Geneseo, Illinois company either, they also borrowed that. This type of logo was used by U.S. armories dating back to at least 1833. The "since 1794" part is a complete lie, it should read "since 1974", again this Springfield Armory Inc, has NOTHING to do with the US. Armory at Springfield, Massachusetts. I did a story on companies that do this sort of co-opting of names and trademarks, read more here.
Glock
The Glock Firearms division was founded in 1980, the font used was probably created by an artist and later copied by several fontographers, the closest being "Pero Extra Bold" or perhaps "Arista Pro Bold".
The font used in the word PERFECTION is most likely Jam Grotesque.
Sources:
Americans: Savage Arms | Smithsonian Institution (si.edu)
More about the Indian Head logo (savageshooters.com)
marlin history (leverguns.com)
History | SIG SAUER
Legendary Innovation (winchester.com)
Our History - Beretta Holding
Colt Logo, symbol, meaning, history, PNG, brand (logos-world.net)
Colt "embattled horse" logo history | 1911Forum
The Marlin Firearms Company Bronze Statue by Sculptor Trace Guthrie - C.O.A. | #2010449937 (worthpoint.com)
I'd like to know the history of the S&W shield placed on their firearms. | Smith And Wesson Forums
Wilson, R.L., (2007), Ruger & His Guns, New York, NY: Chartwell Books, Inc.