Do peach tree seeds need to go through a cold spell before they sprout?

Yes they do. 2-3 months stratification or cold spell is recommended. First let the stone dry for a couple of days, then crack it and get the seed out of the middle. Pop it in a container, seal and put in the fridge to stratify. It won't grow true to type and will be several hears before fruit is produced but could be interesting. Commercially grown trees are propagated by grafting.