Hufe ausschneiden - trim the hooves
Hufe raspeln - rasp the hooves

Leider habe ich noch 'Hufe auskratzen' vergessen.
Vielleicht kann das noch jemand nachlegen.
Vielen Dank!

You pick the hooves with a hoof pick.

Yes, as Helmi says, you pick the hooves out with a hoof pick.
:-)

Sorry Debbie and Helmi, I've to rework it.

I got that: you pick, trim and rasp the hooves.
But these workings all in all are ???

In German I'd say: 'Hufe richten' or 'Hufe trimmen (odd to my ears)'
Is there an engish phrase? Could it be 'trim' as well?

Thanks for help!

@ # 6, these are all tasks a farrier does when he shoes a horse or resets the shoes. so the general term would " horse shoeing tasks."

Thanks Helmi!
Even if they get no shoes on?

If it need not sound so technical, you could also simply say "hoof care/maintenance"

@ # 8, no shoes?
Horse pedicure - as simple as that. :-))

@#9 Thanks for the alternative.

@#10 You're kidding, Helmi. That sounds odd!

hoof care

Thanks Debbie, that fits.