There's also "wild swimming" [1], swimming in natural waters. From a Nordic perspective there's little "wild" to it but apparently it can be an exotic experience in other countries. I wouldn't be surprised if "wild running" was a thing somewhere, after all in many places like England finding an actual forest to run in can be highly nontrivial.

[1] http://www.wildswimming.co.uk/

I don't understand, is there a way to assume you would swim in something that's not natural?

For me, in Brazil, surrounded by waterfalls and beaches it's not only common but also necessary for you to relax sometimes.

I think the distinction is between places in the wilderness (peaceful) and tourist beaches (not-so-peaceful).

I think in the UK both waterfalls and beaches are in short supply.

There’s quite a few beaches in the UK, https://www.thebeachguide.co.uk/south-east-england/.

Where I live I know many people who do both of these things (including myself). But we're surrounded by water and forest! It makes good sense to get out into it. I have a 7mm wetsuit so I can swim year round.

I’m curious, do people create elaborate illustrations on the ice or make any other use of it?

What’s not wild about running through an actual forest?

The forest could have markers indicating the track, could have bridges built to cross small streams, or even parts with paved (gravel or worse) paths.

Indeed, if the forest had not been tamed, not had some part of it claimed from the wild, it would be neigh-impossible to run in it.

That depends a bit on the kind of forest (some forests have way less ground cover than others) and on how you define “forest” (e.g. if a river that floods regularly flows through a forest, do you consider its shores to be in the forest?) and “running” (e.g. are the Barkley marathons (https://en.wikipedia.org/wiki/Barkley_Marathons) a running race?)

Good points, so the ice skating is a bit more wild with this perspective, if it's an "untamed" lake. (There certainly exists tamed lakes).