We have a Ritual ceremony that can only be done outside since there's a lot of fire involved. It's a public ceremony, but my chapter chooses to do it privately.
Nonetheless, here's an example of what it can look like:
As for initiation, we had done it outdoors a few times. There was only 1 small thing that needed an indoor element, but we easily made due since we're resourceful. I love it outside, actually. It's still serious and meaningful, but more relaxed.
And yes, we do that on private property, far from the public.