There is no H. P. or Horace P. Smith listed. There are several Horace Smith's and the closest one matching your information would be:

Horace Smith
Regiment Name 19th Virginia Infantry
Side Confederate
Company I
Soldier's Rank_In Corporal
Soldier's Rank_Out 1 Lieutenant
Film Number M382 roll 51

others are:

Smith, Horace
Confederate Cavalry 7th Regiment, Virginia Cavalry (Ashby's)

Smith, Horace
Confederate Infantry 21st Regiment, Virginia Infantry

Smith, Horace
Confederate Infantry 55th Regiment, Virginia Infantry

Smith, Horace
Confederate Cavalry 15th Regiment, Confederate Cavalry

All were Privates.