Wool On The Beekmantown Road

Source

In the evening of the fifth instant [September 1814], Major Wool was ordered forward with his corps, to support the militia on the Beekmantown road. It was designed to reinforce him with two pieces of artillery, before daylight; but the officer having charge of the guns did not join him in season. At early dawn on the sixth, the enemy were in motion. The column on the Beekmantown road, consisting of the divisions of Generals Power and Robinson pushed forward with great rapidity. Major Wool and his men withstood them for some time with matchless hardihood and bravery, killing Lieutenant Colonel Wellington, of the Buffs, the leader of the advanced parties; but the militia were seized with an unhappy panic, occasioned, in part, by the red coats of the New York cavalry, stationed as look-outs on the hills; whom they mistook for the British soldiers. The firmness and intrepidity of Major Wool and his command failed to encourage them, and their premature flight soon compelled him to retire. [Source] 

Wool's actions from another source.

Hero On A Horse

From The military heroes of the war of 1812: with a narrative of the war  by Charles Jacobs Peterson:

William Gray Simms

Tyler's quarterly historical and genealogical magazine, Volumes 1-2:

William Gray Simms was born in 1795 and died in 1867.  He served in Bunch's Regiment, Mounted, in the War of 1812.

More about Bunch's Regiment:

"Colonel Samuel Bunch commanded two separate regiments at different times during the war. This regiment of three-month enlistees, in the brigade of General James White, participated in the action against the tribe of Creeks known as the Hillabees."

Driven Off By The Cavalry

From The military heroes of the war of 1812: with a narrative of the war:

"...Lieutenant Colonel Campbell of the 19th infantry was dispatched...against the Indian towns on the Mississinewa river.... . On the seventeenth of November he surprised a village inhabited by Delawares and Miamis... ."

"Just before daylight the next morning they were attacked by a party of Indians three hundred strong.  A desperate contest was kept up for nearly an hour when the enemy were driven off by a charge of cavalry....". [Source]

Troops Furnished

Source

Thomas Hinds

Source

"Thomas Hinds [1780 - 1840] became first lieutenant of the Jefferson Troop of Horse."  "His marriage [to Malinda or Leminda Green] strengthened the already warm attachment between himself and General Jackson, with whom he was in after years to come in close contact in some of the most thrilling episodes of...history...". Source

From Thomas Hinds' biography at Jefferson County, Mississippi, GenWeb:

"After the Battle of New Orleans, General Andrew Jackson said of Jefferson Troop of cavalry and its commanding officer Thomas Hinds, 'the cavalry excited the imagination of one army and the astonishment of the other.'”