I live near Deming NM. I have been trying to find out what artillery pieces where used at Camp Cody. I have a number of the expanded shells from the area they were using as a firing range. The shells are very rusty but I think they measure 3 inches.
In as much as Camp Cody had such a short life( 1917-1921?), the casing you've found are almost certainly 75mm. The field artillery system in service at the time was the 75mm M1902. It was an effecient weapons system( design collaberation with the German firm of Ehrhardt is clearly discernable ), but was substituted for by the M1897 upon America's entry in the war. The US high velocity 76mm would not be developed for another two decades.