A small outdoor sauna is the answer for a yard that will not take a cabin, and the good news is that the smallest real outdoor saunas are genuinely small: a two seat barrel or a compact cube takes up about the footprint of a garden shed and needs no plumbing at all.
What actually fits
A two person barrel is roughly the length of a small car and narrower. A compact cube cabin is tighter again in plan but taller. Both want clear space around them for airflow, for the door to swing out and for you to walk round when the cladding needs attention. Measure the working space, not just the body of the cabin.
Setbacks and the neighbors
Small does not exempt you from local rules. Many jurisdictions have setback distances from boundaries for an accessory structure, and a wood fired stove brings fire separation and sometimes a permit into it. Check before you order rather than after delivery, because a cabin that has to move is a crane and a weekend you did not plan.
The base is the same job
A small cabin still needs a level, drained base that stays level. Gravel with pavers under each cradle or bearer is the usual answer and is not much less work for a small unit than a large one. A base that settles puts a barrel out of true and a cube out of square, and doors stop closing either way.
What you give up
Lying down, mostly. A two seat outdoor cabin seats two upright and takes one lying with knees bent. Heat-up is quick and running cost is low, which is a genuine advantage. The other trade is the changing space: with no vestibule you undress in the weather, which decides how often a cabin gets used in a cold state.
Questions people ask about small outdoor sauna
How small can an outdoor sauna be?
A two seat barrel or compact cube is the practical floor. Below that you are into tents and pods rather than cabins.
Do I need a permit?
Often for the structure and usually for a wood stove, and setbacks from boundaries commonly apply. Check locally before ordering.
Is a small cabin cheaper to run?
Yes, noticeably. Less air and less timber to heat means a faster heat-up and less energy per session.