There were a lot of guns taken west with those who followed the California Trail or the Oregon Trail to the Willamette Valley. There were also many accidents -- one common type due to the style of weapon. Flintlocks and percussion muzzleloaders, with external hammers. Remember there were no interstates back then or parks and once you got off the "Oregon Tail" (which was well marked by wagon train ruts some made in rock and STILL THERE TODAY) you were in the wilds. Pulling a rifle through brush sometimes caused a branch to snag a hammer, or trigger, and
*BLAM!* Ol' Trader Sam got it in the hindquarters. Or the gun owner.
It wasn't uncommon to have several guns as the quickest reload was a second or third gun, especially prior to repeater rifles. Throwing them away? No,
not while you still had transportation, for sure.
Hunting buffalo pretty much became a specialty of buffalo hunters who prefered the big bore Dropping block or rolling block guns in .50-110 calibers but much of this really happened later in the 19th century. Those following the trails hunted deer, rabbit, and other food animals which would probably only rarely include buffalo. Bears were always good for their furcoats.
It's said that it was the "Winchester" rifle that won the west. In the decades after the Civil War they did become more prevelant, but prior to it was all muzzleloaders. Even after the repeating rifles, the Henry, Winchesters, Spencers, Kennedy Repeaters, Marlins, etc. came out they were often scoffed at by real hunters as they usually used what we consider pistol caliber (the .44 Henry Flat was powered by 26 grains of BP and not shockingly powerful, its successor the .44-40 only slightly more impressive). The Sharps and Remingtons in their singleshot capacity but using the large ... "antiaircraft"
shells were more loved by the hunters -- especially those after buffalo.
But the idea of people tossing away guns is silly. Losing them through accident? Sure.
There's a lot of photos extant of people who went off west, who had that photo made to send to family who were staying behind. It's not odd many of these showed the person holding a flintlock, or percussion rifle or shotgun. They were saying
"don't worry, I'm prepared to defend myself, my wife, my children."