Never mind my indoor ice rink pipedream.
If you live in a place where the weather is cold enough to freeze water - you may be able to make an outdoor ice rink reasonably cheaply.
I've been told that in many places up north, its very common for people to build ice rinks in their own backyard. They level the surface, build a wall around it, and usually install a suitable liner (available online) so the applied water doesn't seep into the ground before it freezes.
Someone who used to skate on outdoor ponds and lakes told me that, if you don't have an ice surfacer (e.g., Zamboni), ideally you want to form the ice by applying many thin layers of water to the surface at about 20 degrees F or very slightly above. Below 20 degrees, and the ice freezes before it has a chance to get rid of the bumps.
Of course, when it rains or sleets, nature will mess up your surface, so you might want to build some sort of roof over your rink. It is also common to suspend some sort of small mesh over it to prevent it from melting when it gets slightly warmer. And you need something like a large wide squeegee to push surface water out of the way. And if the solid ice layer gets too thin or soft, it isn't safe to skate.
You have to get used to outdoor ice - weather conditions vary a lot, and so does the ice.
BTW, our facility has one outdoor ice surface. Staff spend a LOT of time and effort maintaining it, and most skaters prefer indoor ice.
There are lots of more detailed instructions online for making and maintaining outdoor rinks, from people who have actually done it, and companies that sell supplies for it.
AFAICT, in most places, a rink that other people can get to is an "attractive nuisance", just like an outdoor swimming pool. If someone hurts or kills themselves on it, you may be liable, even if you didn't give permission for them to skate. So people sometimes fence the area off in an effective way, though that might not stop everyone.
OTOH, if you travel to someone else's reasonably well maintained rink, you don't have to bother with making and maintaining your own, or worry about liability. That's what community and commercial ice rinks are for.