To say thats a good idea or if it will work? You can't. It all depends on the location, History, and Audience it attracts. If people aren't paying for something currently they're not going to want to have to start.
Start off do the research.
I'm not sure if you're asking "how do I crowdfund?", "should I crowdfund?" or "what are the best methods to do my crowdfunding", but I'l do my best to answer.
Assuming you have a database (with emails) of previous clients, then your best option would be to crowdfund with the 'prizes'/returns being a membership (at various levels) at the ice-skating rink. This creates a win-win situation for both sides. If you don't have an email database, then perhaps first start creating one, because you need a minimum amount of first pledgers/donations for the campaign to gain momentum.
P.s.: I believe in being open and honest, so no offence, but before running the campaign, I strongly suggest that you make some changes to the ice-rink itself. I looked at the website and the photos, and both are not very inviting. Whilst your website can wait, the rink itself needs some work - it has to be an amazing experience for kids and adults a like. A few suggestions (at a minimum budget) (you might already be doing some of these):
1. Pick a theme (for example Hollywood) and add posters all over with that theme - you can get Hollywood movie posters for almost nothing today.
2. Add some colored lights and turn off the regular ones.
3. I saw speakers, so make sure you're playing cool/fun music.
4. Create theme days on the rink - dancing day, sports day (ice hockey), lovers/romantic day for 18+, outing days for businesses (create a program for companies who want to bond their team-members..). Lots more ideas.
5. Add some complimenting attractions/services for both kids and adults (this is also good for up selling): comfortable sitting area for adults (some old, but nice looking sofas), coffee machine/stand, Cotton candy stand, charging area for phones (in safe) for a small fee.
the place has to have the cool/fun affect.