How do you marry Won at harvest moon more friends in mineral town?

You have to complete all the marriage requirements:

Upgrade your house twice

Buy the Big Bed

See four of Heart Events

Have a Red Heart with him

Then you can propose with the Blue Feather.

To raise Doctor's Heart color give him a gift he likes everyday. His favorite gift is Milk. He likes Herbs, Juices, and Bamboo Shoots.