Club-run freestyle sessions are more likely to require a membership card than rink-run freestyle sessions. Rnks in some areas of the U.S. do ask for a card to discourage skaters who might be a hazard on the ice, such as rank beginners. This is more likely in areas with a large figure skating population and limited I e, which means "all level" freestyles in lieu of separate high/low/Moves/dance/etc. sessions.
Check with the rink's figure skating director about the requirement. You might be able to take out a $25-ish Basic Skills membership with the rink's program or an individual ISI membership for $15. The individual usfsa or club/usfsa memberships are pricey and not worth it unless you're going to test or compete.
Clubs tend to want the membership for insurance purposes so if the Club runs the freestyles, ask the membership chair about the options. They may be able to register you as a Basic Skills member if it is required.
To be honest, most rink clerks don't bother checking for cards, even if it is posted. If you look like you know what you're doing when you stop to pay/punch, they won't blink. I was only "proofed" once-it was in Colorado.
one major caveat: self-taught skaters can be downright dangerous to skate with on any session. You would do well to be honest with yourself and correct any dangerous habits (skating backwards without watching where you're going, for example,) learn the rules, observe some sessions, and be considerate of other skaters.