There are a few issues to consider.
You can take all the pictures you like in a National or state park. There are also no restrictions on using images of people that are taken in any public place. Some people think you cannot use photos with people unless you have a release from them. It is actually true that you do not need releases for pictures taken in any unrestricted public place, i.e. along trails, walkways, etc. in a public park, where there is not an expectation of privacy.
You could think of these as default conditions. Laws, restrictions, and "conditions of entry" can be put in place to alter the defaults. For example you might go to a concert and on your ticket it says photography is not allowed. Some National parks have begun charging fees for photography if people are explicitly coming to take pictures for an event, like a wedding.
http://www.washingtonpost.com/wp-dyn/content/article/2006/06/08/AR2006060800182.html
They also ask that you obtain a permit if you are doing anything out of the ordinary when you are taking pictures. See their policy here: http://home.nps.gov/applications/digest/permits.cfm?urlarea=permits
I have not yet heard of such a thing at any state parks yet.
Anyway, my point and the answer I would offer to your question would be: It depends on what park you are going to and what kind of photography conditions they may have in place. Snoop around the park website. Look over any material they give you when you enter the park. If there is nothing that says anything about taking the type of pictures you are taking, don't worry about it and take all the photos you want.
I would guess you should not run into any problems though, at least in seeing the short description of what you are planning to do.