You're sort of correct. A gelding or mare that has never had foals needs to be placed in the garden before the overnight update to remain on the list to be put into the memorial garden. If a horse has some living decendants then they won't be removed during the update, and will still appear in the drop down list to add or remove.

Since this happened today after the daily update scripts ran your horse should have been able to be placed in the memorial garden before tonight's script update.

*Winter Equines* said:

I might be wrong, but I think the horse should have had some living foals (or dead foals with living foals) to appear in there, but I don't own a memorial garden and have never owned, this is just something that I think I've heard, but I might be wrong