It is a wonderful idea to see the program in action. It is in the best interest of you and the program you attend that you like it! Some universities have designated times of year when they host a "getting to know us" session. Personalized visits are often also able to be arranged. I am unfamiliar with programs that would allow you to participate directly in normal session classes. There is a liability issue, as you said, but there is also a duty to create a safe and consistent learning environment for the registered students that would be breached if others were regularly participating in class. Some programs may offer special open classes that are intended to allow prospective students to dance with the current students. All this being said, it should be acceptable to politely ask about their policy/opportunities to dance during the visit.
Watching a class or many different classes is often permitted. I think this is a great option because it could potentially allow you to see numerous concurrent classes in a non-threatening manner. Dancers learn so much from watching, and I think you may be surprised at how much you could absorb when you are observing a program. Additionally, your mirror neurons will be working and you will be able to get a good sense of what it would be like to be in that class (for info on mirror neurons and even how mirror neurons relate to dance, check out http://www.pbs.org/wgbh/nova/sciencenow/3204/01-resup.html
for starters. Pub Med, a free biomedical search engine, has detailed scientific literature about mirror neurons if you want to really dive in: https://www.ncbi.nlm.nih.gov/pubmed/).
Additional things to ask/consider: are there current students that you can talk to (informally during the visit or formally by some outreach group)? Can you time your visit to coincide with a departmental performance? What opportunities and points of emphasis does the program have? Does the program offer opportunities to grow your mental concept of what dance is and how you want to engage with it?
Best of luck in your decision-making process and in your career!