T.H.
We generally do Saturday. You didn't mention how old your child was, but most people mentioned working around the nap time...that is key, not only for your child but also for the party-goers. We've had a few parties that start at 11am and go until 1 (really more like 2 with our people, but whatever!) and we serve lunch and cake.
If you're not into making a whole meal then I would say do it from like 3-5 pm. The army theme is cute. The suggestion you had of hiding army men around is cute. You could also do a water gun fight (if you're okay with that) and the water gun could be part of their party favor. You can get cheap water guns and army looking hats on Oriental Trading Co...you can probably get some other party ideas too. Capture the flag was also a good idea, but the kids would have to be a little older for that. You could set up an obstacle course and utilize the park for it as well as bring along things like hula hoops they have to jump through (laying flat on ground), crawn through tunnels, etc....just like they do in basic training! The first person to the end could get a badge or something like that.