I don't know about other parts of the US, but now that I live in California again I can say that most rinks around the Los Angeles or San Francisco Bay area are open year round. I lived about 20 minutes from a pretty popular rink for most of my teenage life, though I probably went there less than 10 times before I turned 20. Oh, all the time I wasted...
I caught the "Adult Onset Skating Syndrome" post-Olympics (haha) while I was studying in Denmark. I joined a club there but only for a month since practically all ice is gone in DK after March (although supposedly a rink at the resort park Lalandia is open year round). I barely learned to skate backwards in that time as it was. I scrambled to Malmø in Sweden to practice since they had one ice rink there open until mid April, though I only made it there two weekends.
While I was in Lake Bled/Jesenice in Slovenia I was told by my bed and breakfast host that they had a skating rink five minutes away and I was so excited! LOL too bad she found out it was closed after she made a phone call, but apparently it opened up sometime in August? I know the DK rink I went to didn't even start up again until September at the earliest..
I actually tried to find ice in Berlin in the summer but I couldn't find any open rinks either. It was so frustrating to just get started with skating only to involuntarily go without it for four months! I didn't get to skate again until I came back to California late July and I pretty much had to start over again...