Are there any patents out for baseball caps with pigtail/ponytail openings?
Performing a thorough patent search is a significant effort. Some people make a career of it. I think you should try to do it yourself first and then ask for help if you get stuck. Even though I don't consider myself a professional, here are some tips:
First, it can be useful to do a basic Google search for such products. From this you can see which companies make competitive products. If you see something, you will want to search for that companies patents in particular.
Second, use a patent specific search site. The two free ones I like are Google Patents and The Lens. I especially like The Lens. Initially just put search terms in and see what pops out. For instance using the terms "baseball cap ponytail" and limiting to US documents yielded 82 hits on The Lens. Be careful not to to be too specific. "Cap" might not find a patent which only uses the term "hat". You can refine the terms, limit the search to US documents, etc.
When you find some relevant patents/applications, look at them for cited patents. This will give you some more prior art. Also, experts use the classification codes to help refine the search. When you find particularly important patents, then it is good to use the US Public Pair site for research. Here you can review the communications between the examiner and the applicants, see all the prior art the examiner used, determine the legal status of the patent, etc.
With a few hours of work, you should be able to get a pretty good start on identifying relevant patents. Remember, it is the claims that define what the patent is covering. I usually look at the claims and the figures first.
This doesn't eliminate the need for a professional at some point while pursuing your own patent, but doing a search for yourself will greatly speed any subsequent searches (and potentially save you some money).