We are at ca 750-800m ( I can never remember...) but sort of protected by the Rossberg. That means we get less sun, but are not as exposed as real mountain areas. We are always searching for 'dog friendly' ideas, as the mutts have re-landscaped pretty much all my earlier efforts. So for what it's worth...
Since I have such a small garden, I try to plant 'double duty' plants - things that are useful, like fruit, as well as decorative.
Wild strawberries/Waldbeeren make a great natural ground cover, particularly good on a slope - they spread very quickly. Slugs might be an issue, though.
(Don't plan on eating the fruit if the dogs piddle in the area.

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Vinca is another hardy slope groundcover, fairly resistent to puppy paws. White, light blue or darker blue flowers in the spring, Vinca stays green all year round.
What is your soil? If acidic, my new favorite slope shrub is compact blueberries. The plants grow to ca. 60-80cm, white flowers in the spring, fruit in the summer, the leaves turn red in the autumn. They are deciduous, so will be bare in winter.
If the soil is not acidic, there are two blueberry varieties that tolerate normal soil - Reka and Elizabeth. These will grow taller, however. Ca 150cm, IIRC.
Some blueberries take sun, some part sun/part shade.
Jury is still out on my Johannesbeeren; I've had Blattausfallkrankheit two years running, perhaps we have too much rain and cold for them.
Another easy care shrub is potentilla - small white, pink, red, or yellow flowers mid summer on. These do need some pruning to keep neat, but other than that can pretty much be neglected. Again, deciduous.
If you want year round green, a variety of compact evergreens might be nice. The dogs run through the evergreens, and they do not seem to be any worse for the wear. (Pretty prickly on puppy paws, though.)
You could do a foundation of evergreens with a few other interesting ground covers to hold the soil in - and plant bulbs for spring color. That would be very easy care.
Some of the lower-growing cranesbills make for very easy care summer color.... but be careful, because some varieties cannot tolerat full hot sun.
I've had good luck with Barlauch; a nicely formed plant, white flowers in the spring. And useful. The dogs do not piddle anywhere near the Barlauch; perhaps it's the garlicky smell.
You could even do hardy herbs liked creeping thyme.
If you have strong sun, day lilies are super easy care. Very hardy... but if the dogs run through the area they might sucumb . (The Belltie sleeps in my day lilies. They put up with him, but only just. And he's fairly little - Heffalump would do them in.)
The previous owner planted ferns in our granite wall - another easy slope option. They stand up to dogs, you can absolutely neglect them... until winter. They do not fully die back given our climate, so the ugly brown dead fronds need cutting back. But they can be whacked off with a hedge trimmer if needed. I like the small ferns, but am not so fond of the giant ones - and these have proved almost impossible to get rid of. You'd need something to mix with the ferns, though, as they do not provide any fall/winter interest.
Whatever you choose, look for Hohenlage (no idea what the French is), plants suitable for high altitude. Most of my mistakes come from planting things that cannot take the altitude - even though 800m isn't really high altitude.
Just a few ideas, based on what is in the 'dog' portion of my garden.
Looks like you have lots of fun ahead - good luck!