As the weather starts to warm up, you will likely find that the public sessions are not quite so crowded.
This is very common around here - once it warms up outside, or the spring sports season starts, the attendance drops. I refuse to coach or skate on a Saturday afternoon or Friday night, those sessions just too zany for my taste at any time of the year. Saturday nights are okay, as are Sunday afternoons, throughout the year. They empty out tremendously when Spring arrives.
Check the public session schedule regularly - when one of the leagues' hockey season ends, our rink converts that time to a discounted-price public session. For the first few weeks of that weekday-evening session, there are as many as 12 people on the ice and it's awesome for skating practices. It takes a while for people to notice it on the schedule, but even then, it's never mobbed unless there's a group trip.
You can also check out "club ice" - the skating clubs in some areas rent ice for their members. Those aren't always listed on the rink schedule, but many of them welcome guests for a slightly higher fee. To find out about them, you'll either see "(clubname) Ice" or you have to go to the Club's website/schedule.
Most clubs and rinks will allow a beginner skater on a freestyle if they'll spend their ice time taking a lesson with a coach. If you're going to practice by yourself, be sure any freestyle is listed as "low" or just "freestyle" since you're a beginner. Avoid "Moves," "Dance," and "High" freestyle sessions.
Ask the skating director if there's practice time included with your group lesson. I've coached at several rinks that set up a practice area during the group lessons, coning off one end of the ice. A lot of parents didn't realize it meant the skater could practice for 30 mins, then attend their lesson for 30m. (It was an hour-long time frame with two 30m group lessons scheduled.)
The lack of convenient public sessions during the week is really killing non-hockey skating in the US. Gone are the days when a kid could go skating with friends after school or an adult get in a practice from 7-9pm on a Thursday. You look at rink schedules and all those choice times are rented by hockey leagues, which is why it's growing. They can hire 1-2 professional coaches, add a handful of volunteer parents and fill the ice with kids and cover the rental cost easily. Sorry for the soapbox rant.