Because they were bred to have large horns. It's all in the breeding.
the bighorn has big horns and the longhorn has long horns
Shorthorn cattle (referring to the beef type, not the Milking Shorthorn [dairy]) are thicker, bigger and more bulkier than Longhorns are. Much of the Shorthorn breed are polled, and come in only three colours: red, white and roan. Shorthorns were historically more commonly known as Durham cattle, which had horns that only had a spread of about two to three feet. Longhorn cattle (assuming you're referring to Texas Longhorns and not English Longhorns) come in wider variation of colourations, from all black to dun to speckled black and white or red and white, and near everything in between. TL's have long horns, ranging from 6 to 7 feet in length, more commonly the former and point out and up. They are commonly not as big and beefy as Shorthorns are, being more rangy-looking than most beef cattle. English Longhorns are always a red roan with their horns pointing downwards and in. They are less common in North America than either shorties or TL's.
if the big horn sheep don't have horns then they would have to find a different way to fight over food
For the bull, it's more or less used for self-defense and as a means to show other bulls how big and strong he is. For us humans, a horn doesn't really add much value except, historically, as a place to hold gunpowder and as some sort of musical tool. Today, a bull's horns (especially those from a Texas Longhorn) are merely used as decoration to be hung on the wall.
The bars on a Texas gate or cattle guard act as an optical illusion for the cattle. The bars make it seem that there are too big spaces for their feet to be stable on, and also the bars make it seem they will sink past their knees through the bars. The culvert dug underneath the guard increases this illusion, and so the cattle refuse to cross it.
the bighorn has big horns and the longhorn has long horns
Each individual horn can average to grow up to 3 to 4 feet in length. It's much harder to measure spread since they don't grow outwards from the skull much like domestic cattle do, or like the domestic bovine breed the Texas Longhorn does.
Shorthorn cattle (referring to the beef type, not the Milking Shorthorn [dairy]) are thicker, bigger and more bulkier than Longhorns are. Much of the Shorthorn breed are polled, and come in only three colours: red, white and roan. Shorthorns were historically more commonly known as Durham cattle, which had horns that only had a spread of about two to three feet. Longhorn cattle (assuming you're referring to Texas Longhorns and not English Longhorns) come in wider variation of colourations, from all black to dun to speckled black and white or red and white, and near everything in between. TL's have long horns, ranging from 6 to 7 feet in length, more commonly the former and point out and up. They are commonly not as big and beefy as Shorthorns are, being more rangy-looking than most beef cattle. English Longhorns are always a red roan with their horns pointing downwards and in. They are less common in North America than either shorties or TL's.
After the Civil War Texas ranchers drove cattle in herds to Kansas because that is where the big stockyards were at the time. It was also a place for the Texas ranchers to use the railroad for shipping cattle elsewhere.
Almost all breeds of cattle are born with buds, the ability to grow horns. The horns are almost always removed at a young age. Sometimes farmers allow the cattle to grow horns, depending on what breed they're raising. A few breeds have been developed in which the offspring are polled, that is, do not have the ability to grow horns. Holsteins are naturally horned, so their horns need to be trimmed or cut before their horns get too big, which is when they are a few months old if horn buds can be seen or felt. However, other cows can be born polled or hornless and do not need to have their horns trimmed. Horns is a recessive gene in cattle, so if a horned cow mates with a polled bull, the offspring will be polled. But mating horned with horned produces horned offspring, or hetero polled with hetero polled have a 25% chance of producing horned offspring. The naturally polled breeds of cattle include Angus, Red Angus, Brangus, Red Brangus and Galloway.
Texas and Colorado are big meat producers (Cattle and sheep).
The city of Forth Worth, Texas is the heart of the cattle industry. One of the big attractions in Fort Worth id the Fort Worth Stockyards.
There are a variety of prices for tickets to see the Texas Longhorns play football. The cheapest seats are for students and cost around $15. There are tickets up to $1000 for a big game and in the box seats.
if the big horn sheep don't have horns then they would have to find a different way to fight over food
Because often places like these were the closest points to sell and ship their cattle. They didn't have auction marts or sale-barns nor big cattle-liners back then.
Frog
The big major cattle drives ended around the early 1900s, when the railroads became more and more accessible for ranchers to herd their cattle to. Then came the engine-powered trucks that could be brought directly to the ranches to haul cattle away to the rail station. When that began, then that was officially when the cattle drives ended.