I have worked for trainers and have done some training myself.
Trainers typically use all their own tack/equipment (saddles, pads, bridles, bits, boots, etc.)
The only thing I would recommend sending is a halter/lead, a blanket in case one is needed and any special meds and/or supplements that your horse may be on. I also send a copy of vaccinations/vet records, deworming records and farrier records as well as an emergency card containing emergency contacts of yourself, your work, your family, your preferred vet, shoer, etc in case an emergency arises.
Everything else should be provided.
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