Thank you for your answer :)
If you have a contract for your horse, it's the insured him therefore in case of disaster, he continues to benefit from the guarantees unless otherwise agreed.
It will be necessary to be vigilant on the criteria used to put the contract. For example, if the country of parking was France and that now the horse is in Italy, this can change the deal for the insurer. It is better to check with him to avoid any disappointment.
I hope my answer will help you.