Christian,
There was at least one regular US infantry regiment that was light infantry. John Fredriksen (The United States Army in the War of 1812, 2009, pp. 257-258) notes that when the 26th US Infantry was re-raised in 1814 it was armed with rifles. This is also documented by James Kochan (The United States Army 1812-1815, p. 20) who notes that due to a shortage of the green rifle uniforms, it received the grey uniform like the 2nd-4th Rifle Regiments. Fitzhugh MacCrae's "US Order of Battle, Northern Theater of Operations," which can be found on the Histofig.com website, identifies the 26th as a light infantry unit that was brigaded in Col. James Gibson's 4th Brigade with the 1st and 4th Rifle Regiments during the Niagara and Lake Champlain campaigns from 1 July – 15 November 1814. Col. Gibson's brigade was part of MG Jacob Brown's Left Division. Fredriksen notes that company-sized or larger detachments fought at Fort Erie and Plattsburgh.
With regard to the Rifle Regiments, Fredriksen notes (pp. 280-285) that the Regiment of Rifles (later the 1st Rifles) fought at Gannanoque in 1812; at Elizabethtown, Ogdensburg, York, Fort George, Stoney Creek, Hoople's Creek and Massequoi Village in 1813; at La Colle Mill, Sandy Creek, Conjocta Creek, Fort Erie and Plattsburgh in 1814; and at Point Petre in 1815. He notes that the unit participated at Gannanoque and Point Petre in company-sized detachments, and at greater strength than that at the other actions. His text goes into more detail, but as a general conclusion from what I have read, it seems 2-5 companies were likely present at the other actions. Fredriksen also documents the 4th Rifles participation at Conjocta Creek, Fort Erie and Cook's Mill in 1814 (pp. 288-290).
Fredriksen also writes (p. 177) that "due to the shortage of horses and cannon, the Regiment of Light Artillery frequently fought as light infantry."
But this only scratches at the surface of the question. To gain an understanding of what forces were used as light troops and how they were used, it is really necessary to consult the available memoirs, diaries and letters of the participants. I recommend the recently published The War of 1812 in Person: Fifteen Accounts by United States Army Regulars, Volunteers and Militiamen, edited by John Fredriksen (2010) as a starting point. Although I will be cautious and note that the subject requires more detailed reading, the working impression I have reached is that the US Army task-organized (to use a modern concept anachronistically) light infantry formations for each campaign from various regiments. They were used in a manner consistent with light infantry formations in other armies: pickets, advance guards, assault forces, rear guards, etc. Le Coutuer's diary (Merry Hearts Make Light Days: The War of 1812 Journal of Lieutenant John Le Couteur, 104th Foot, Donald Graves, ed., 1993) offers some vivid descriptions of skirmishing against Americans. (I remember his mentioning the Rifles, in particular.) Le Couteur commanded the light company of the 104th New Brunswick Regiment.
Here are some specific examples taken from Fredriksen's later work. (I apologize but since I am working from an e-book copy, I cannot give page number references.)
Lt. Col. George McFeeley's diary describes the formation and operations of a composite light force of about 600 men for the assault on Fort George on May 26, 1813, that consisted of two companies of rifles, and multiple companies of the 22nd Infantry and the artillery, one gun and some dragoons. Scott commanded the overall force, and McFeeley was second in command. Scott took tactical command of one company of rifles, Hindman's, Stockton's and Biddle's companies, the artillery piece and the cavalry. Now I know from other reading that Hindman and Biddle commanded companies of the 2nd Artillery (Scott's regiment). McFeeley took tactical command of the other company of rifles and four infantry companies commanded by Capts. Nichol, Mills, Milliken, and MacFarland. If the division of the composite force was done on regimental lines, this organization would imply these four companies were from McFeeley's parent regiment, the 22nd, and that Stockton commanded an artillery company. At least two companies were from the 22nd, as attested by the next two memoirists.
Major Jonathan McKearsley describes how the advance on Stoney Creek about two weeks later after the assault on Fort George was led by Forsyth's riflemen (1st Rifles), two companies of the 22nd, and four companies of the 2nd artillery "acting as light infantry." The pickets for the entire force were taken from these companies.
Col. Cromwell Pearce's memoir of his regiment, the 16th Infantry, notes that "the light troops, consisting of the artillery, Forsyth's Rifle Corps and two companies of the 22nd commanded by Colonel Scott, led the advance" on Fort George.
Other memoirists and diarists, including Major General Izard, wrote about the operations of a "Light Corps" during the Chateauguay campaign in 1813. Charles Fairbanks' memoir of the campaign states that it comprised nine companies organized in three divisions. Fairbanks was a private in the New Hampshire Volunteers. Izard's diary notes that at the end of the campaign on November 5, 1813, "the Light Corps dissolved yesterday and joined their respective regiments."
Others wrote about Brig. General Macomb's "Elite Corps" during the Crysler's Farm campaign in 1813. A letter of Capt. Rufus McIntire's describes it thusly, "It was composed of the Rifle Corps of about 150 or 300 under Major Forsyth; the Albany Volunteers under Major Herkimer about as strong; a detachment of the 20th Regt. Infy and Richmond Volunteers under Col. Randolph about as strong; and five companies of the 3rd Regt. of Artillery about 300 or 350 strong under the brave Col. Scott of the 2nd Regt. Arty. . . . This corps instead of a reserve was now to be in advance – a kind of standing van guard and were to take the lead in every thing that looked like difficulty or danger."
General Bissell's report to Izard for the Battle of Lyon's Creek in 1814 (quoted in Pearce's memoir) notes that the "Light Corps" at that battle included rifles and "the two elite companies under Captain Dorman, 5th, and Lieutenant Horrel, 16th Infantry."
Pending more research, one conclusion that emerges from this is that multiple company detachments of the 20th and 22nd regiments were designated as light infantry at least some of the time.
One closing thought, as Colin (Caldwells Rangers) noted in his posts, the American state militia regiments included light infantry units. I would add that the state volunteer regiments also included light infantry that weren't necessarily identified specifically as such, but were used in that manner. These volunteers included mounted infantry units like Johnson's or Coffee's from Kentucky, Tennessee and Mississippi that were distinguished for their hard fighting in the old Northwest and the Gulf Coast states.
Rick