High and heated sports room next to the garage? - Ideas wanted

where you drive the gate up in the morning in good weather and sit outside on your AirBike or something. That's why we actually don't want a basement fitness room.

Well, that's just hard to translate: in California you have worst case 15° in the morning and not like here -5° or less.

Is it probably forbidden here in Germany, what is standard in the USA, that people set up a small gym in the garage and do sports there 1-2 hours a day?

Not exactly forbidden. If you build your garage on the boundary line, that's a privilege granted among other things only to garages but not to every use. Even if you prove the garage as a necessary parking space, you are actually only allowed to park a car, tires or a motorcycle there. But not just set up a gym. So provide the necessary parking spaces plus a non-boundary garage/shed or whatever. By the way, there are also inexpensive kits for wooden garages for motorhomes, i.e. well over 3 meters in height. Or you commission a carpenter right away. But I would definitely have this shelter included in the building application by the architect, for example as a "garden shed".

Now I also know what was meant by [Grenzgarage]. No, due to the relatively large plot of land, we do not plan to build directly on the border. And as mentioned, one might be satisfied with a height of 2.8 m.

PS: Yes, of course, we don't have the climate of California or Florida here, but when the weather allows, there is nothing better than being able to do your exercises in an open garage or even in front of the garage.

Thanks again to everyone so far.

nothing better than being able to do your exercises in an open garage or even just in front of the garage.

You link your dream to what you know or have seen in another country.
However, you don’t have to imitate it if "an entire country" or "other people" misuse their garages.
There is definitely something nicer, namely a room built exactly for these purposes with... no, not a roller door that lets air and leaves in at the bottom while you still look at a sheet metal roller door at head height, but rather a nice window or patio door that lets light in even when closed.

It is probably forbidden here in Germany, which is standard in the USA, ...

Well, here in Germany we should comply with the rules of our country
Funny people, the Americans, doing sports in dark garages or linking the sport to the garage building when you have all possibilities.

Yes, retrofitting such a garage with insulation and plastering it and then briefly heating it up to 15-18°C with a radiant heater or some other mobile heating should be well below the costs of about 50k.

The question remains whether you can afford a basement, house, garage(s), and sports area (whatever that may be).
And since I still wonder how someone can call a sports area and a windbreak in the same breath, you should simply start by roughly planning the actual house, so you can then see where the best place and view for the extension is. Because even if sport is your main focus right now, life and priorities will change and sports after gardening anyway.

The solution is a (cold) conservatory with the appropriate height. I would say 25-30K€ should be enough for a really awesome piece. More nature view and morning sun is not possible, even in winter.

Cold winter garden is a good idea - you probably still need a few solid walls to attach equipment, right? Infrared heat radiators from above are suitable for heating. They warm the athlete when he is in the room and are then turned off again. The idea of a sports room is really great. Every little animal has its fancy.

You have the exterior wall of the building. With a suitable design, a side wall could also be created if there is additional demand for mounting on the wall.