In doing more research on
www.baseball-reference.com, I have just discovered that the Texarkana minor league team from the same league as Denison (Texas-Oklahoma League) was not part of that league's standings in 1912 but only 1913 and 1914. This is relavent because one player pictured in the Denison team photo has the same style uniform with Texarkana spelled out vertically going down the chest.
Based on this information, the only possible dates for the photo can now be narrowed down to 1913 & 1914 with a great deal of certainty.
Now even more so, what are the chances that a player looking nearly identical to Hornsby played on the 1913 Denison team? Even better, a player looking nearly identical to Hornsby playing on Hornsby's 1914 team but not being Hornsby?