This is a question with an easy answer but a longer explanation!

The answer is you dont hear about them because they didnt exist! From 1775 until they traded in their horses for vehicles in the 1930's and 40's the US Army almost exclusively fielded what were called or equipped as Light or regular Dragoons.

The US, either as colonies pre Independence, or after as a young Republic lacked many of the cultural aspects, and strategic needs, which would lead to a robust heavy cavalry force. There was the fact that much of the interior of the nation was relatively remote, wooded, and broken, poor cavalry terrain though growing settlement was improving that. There was also the lack of a strong insular upper social class that would dominate the leadership of and help support Life Guards, Horse Guards, etc, and for long decades, the land east of the Mississippi was only spotted with sufficient horses in size to effectively equip heavy cav, and remounts were always an expensive cost for a budget conscious nation sensitive to a large standing army.

That isnt to say none of those factors existed at all. Indeed much of the early cavalry Washington had at hand was from colonial militia units like the City of Philadelphia Light Horse troop, but even then still they were light cavalry. Even at that stage though while Washington accepted the need for some cavalry he was distrustful of too large a mounted arm. Often they were hard to supply with fodder and remounts, and many new or volunteer units lacked the discipline for mundane tasks like forage escorts and scouting or screening. Even here we see the Congress authorizing 4 regiments of Light Dragoons along with a few state units, and while some like the 2nd Light Dragoons, earned a good reputation, problems still remained. There were issues with recruiting enough men, training them to operate effectively, and to pay for them either watching the British in NYC or in the active Southern theater. So many of the units were consolidated into combined arms Legions with a much harder focus on the role of mounted infantry to ride to the fight then do their work on foot, famous commanders like the Pole Casimir Pulaski, Light Horse Harry Lee, and others would lead these units to make up for the lack of true cavalry in the second half of the war. While on the other side, despite constant supply problems the British Army demonstrated themselves that cavalry could play a meaningful tactical role in pitched battles in America, Tarleton's cavalry at Camden, and his own defeat at Cowpens were as impactful as the weeks of small skirmishing in the Carolina's though these too were mostly varieties of Dragoons and Legions.

Postwar though virtually all these units were disbanded along with the rest of the Continentals. There was to be a Dragoon component of the Legion of the United States in the 1790's but these were scrapped when the Legion was too and in its place the Army of the United States had some authorized dragoon companies but were never formed. It should be noted though that the various state militias did have units, and on the Frontier mounted riflemen could and did provide a useful quick reaction force to fighting with native tribes-people. Even the War of 1812 saw only temporary units formed, and a reliance on short term and state units, again mostly Dragoons still.

It would not be until the early 1830's that the US War Dept and Congress got serious about having an established cavalry arm. With westward settlement continuing and into the much more open West, protecting that called for detachments of troops that could move quickly, meet hostile tribes, and defeat them with massed firepower when possible. So in short Dragoons, and while first it was to be a Battalion of Mounted Rangers, but issues with the unit recruited from surly individualist frontiersmen meant it was soon reorganized along more traditional military lines as the First Regiment of Dragoon, United States Army in 1833. This is the unit to which today's modern armored cav 1st Cavalry Regiment traces its lineage. Armed with Prussian modeled sabres, pistols, and early model breach-loading carbines the unit was sent West and in 1836 a 2nd Regiment of Dragoons was formed to split the workload. The units saw action in Florida across the West and in the War with Mexico. During the war a Regiment of Mounted Rifles was also added, these men used percussion rifles, and ditched the sabre, but did much the same work in clearing and policing the route West and newly acquired territories in the 1840's.

While the war offered only a few chances for mounted cavalry charges the 3 units did provide important service as detachments, dismounted infantry, or in seizing California.

By the 1850's sectional violence, and further settlement drove the formation of 2 more regiments, this time the 1st and 2nd US Cavalry. However they were essentially armed with leftover Dragoon supplies, just with altered uniforms, and the now famous Colt Navy pattern revolver, sabre, and a hodgepodge of carbines. And on the eve of the outbreak of the Civil War a 3rd regiment was added and then the 6 existing regiments were numbered as the 1st-6th Regiments of Cavalry from the date of their formation.

The Civil War saw by far the largest massed usage of horse cavalry on the American continent, and the most variety. Of the 100's of state units raised a handful were equipped as Uhlans and Lancers though many were equipped more traditionally after some time in service. It also demonstrated both that the American continent was suitable to mass mounted formations, and that American cavalry could eventually serve as an effective part of the combined arms team to force decisive action. Though while men like Stuart earned glory as Cavaliers of old with daring deep raids and a few heated clashes with their opposites, its arguable that the lack of heavy shock cavalry hurt both sides in not being able to truly exploit tactical victories. Though by the end men like Bedford Forrest, and Sheridan had taken the usage of cavalry as mounted infantry to an art form. In particular Sheridan's cavalry led by men like Custer were instrumental in slowing, stopping, and seizing supplies from Lee's Army of Northern Virginia in the Appomattox Campaign which forced his surrender.

Following the war an additional 4 cavalry regiments were retained making it 10 total with the 9th and 10th being colored units nicknamed the 'Buffalo Soldiers' in time. While the Spencer and eventually assorted makes of Springfiled repeating rifles became the main long arm. The force though was almost totally dispersed across the Plains as a policing force and units larger than a battalion/squadron were incredibly rare with the company/troop level the most common. Even war with Spain and service in the Philippines basically continued the existing pattern. The cavalry's high point at San Juan Hill was made by the 1st US Volunteer Cavalry (the Rough Riders), the 3rd Cavalry, and the 10th Cavalry was made dismounted as infantry, while at the low point Col Custer and the 7th Cavalry troops with him dismounted to try to make their defensive stand when the size of their foe became clear at The Little Bighorn.

In the end the US Army adopted the cavalry that best met the needs of the nation, which for the vast majority of its existence as a mounted branch was as a mobile policing force and quick reaction part of a combined arms team that was eternally short of funds and in parcel packets in small posts. Hence the almost exclusivity of Dragoon or derivative units.

For more straight from the horse's mouth I would first check out this article on the history of the United States Cavalry from the Office of the Chief of Military History, US Army. Its a bit old, being from the late 60's but for our purposes in fine: https://history.army.mil/books/Lineage/arcav/arcav.htm

This page from the National Park Service also has some wonderful photos and sketches of the weapons(sabre, pistol, and carbine) that equipped the US Dragoons for decades. https://www.nps.gov/fosc/learn/education/dragoonweapons.htm