Gentlemen...
My research includes 1LT A. J. Smith during his Mexican-American War service with the "Mormon Battalion" of federal volunteers.
I too have seen the nickname "Whiskey" applied to him and found your thread whilst looking for its origin. Would appreciate any further information you develop on this subject.
My current work is to publish the journal of Dr. George B. Sanderson, Assnt Surgeon for the Mormon Battalion. Smith and Sanderson got a late start from Ft Leavenworth because the Battalion's recruiting commander, Capt (Lt Col) James Allen managed to die before taking the field with his unit. Smith and Sanderson overtook the Battalion at Council Grove (KS) where Smith was able to convince the Mormons that he should temporarily be given command and lead the unit to Santa Fe. The expectation was that Gen. Kearny would there appoint a new Army commander.
In Sanderson's journal there are a few mentions of AJ's drinking habits. The first is from the entry for 25 August 1846: "Smith made a very important discovery after we arrived in camp and that was a bottle of very fine old whiskey as a matter of course it was attended to." Source: Sanderson, George B.; Journal kept by Dr. Geo B Sanderson Ast. Surgeon United States Army from Fort Leavenworth Missouri to Santa Fee New Mexico and to San Diego Upper California and back to the United States in the years 1846 + 1847; Acc2134; George B. Sanderson papers, University of Utah Manuscript collection; Henson, Kevin ed., unpublished transcription, Feb 2014