Veterans can really be any age. If you enlist at 18 and serve four years, you're 22 at discharge and you're considered a veteran at that point.
I think you have to consider the fact that, after the Vietnam era, this is a volunteer military. I don't work with a lot of commissioned officers so I can't speak to that group, but many of the veterans and service members I have met either enlisted either directly after high school or only completed some college. Many times they have grown up in rural areas or small towns that would skew conservative. Plus you are basically taught during service not to question authority. Based on my general experience, it's not a surprise that veterans would more frequently vote Republican.