When it comes to day to day training, yes, in most cases, it's up to skaters and their families to decide what they want to do, assuming their rinks are actually open and in the context of whatever restrictions are in place per local laws. When it comes to comps, it likely won't be up to the skaters - the ISU has to decide whether to hold the comp to begin with, based on health risks as well as feasibility. If a country scheduled to host an event is on lockdown and won't allow it, there goes the event. If a critical mass of countries won't allow their athletes to fly out and/or even train, then comps aren't likely to happen regardless of what risk the athletes are willing to accept.
As of now, the ISU has canceled all events - judge seminars, etc - through mid-August. I think June 15 is their decision date for the JGP? Their process for that should give us insight on what the upcoming season will look like.