May one place a saddlecloth on a donkey on Shabbat itself (without tying)?

Synopsis

One may place a saddlecloth on a donkey on Shabbat for warmth, provided one does not tie it, because tying requires leaning on the animal (using a living creature). On a horse, even placing it without tying is prohibited because the horse does not suffer from cold.

Early Acharonim
Lenient
Strict
Lesser cited
Major authority

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