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keep checking the public coverings for one from a Snowflake. As he is the only stallion she can breed with.

You can also write on the top of your presentation that you're looking for a covering and then congratulate the players which own a Snowflake.
They might see it and offer you a covering/message you if there are none in public coverings.

You can check the Directories > Horses > Divines for players who own Snowflake. And then ask for a cover.