How do I heat my basement using a wood stove on the ground floor?
There's two questions here. 

1) Will my pipes freeze in my unheated basement?


Probably not. Provided you don't have a lot of the foundation wall exposed to the air outside, the basement will likely always remain above freezing due to ground temperature. Ensuring that you properly insulate the stud bays and the like will make that even less likely to freeze.

2) how do I heat the basement with a wood stove above it?


I'm not sure that you can short of there being perhaps some sort of duct-work system designed for wood stoves where you could force warm air into the basement. 

The alternative would be to move the wood stove. Put it in the basement allow it to heat from the lowest point.