Flue pipe/ exhaust height

In a regular wood stove, draft seemed to work best if the flue pipe extended higher then the peak of the building it was in.  Is this true for a rocket mass heater? My building has an 18 ft peak. I planned on coming out the wall close to ground level. Do you think I need 20 feet of pipe? I was concerned all the cold air on it would have negative effects on draw, but 20 feet of double insulated pipe would be freakishly expensive. Any thoughts?

An RMH will absolutely benefit from a tall, warm chimney. A full height cold chimney could be problematic as you describe, just as it would make starting a woodstove difficult. Your best bet by far is to go up inside the house and exit near the peak of the roof, keeping every bit of heat for the house and keeping the chimney comfortably warm. The concept of the RMH is to harvest all the heat before sending it outside, so the exhaust will likely be around 100-200F instead of the 350-500F of a woodstove, with correspondingly weaker draft generated by the chimney. The push from the internal heat riser "chimney" helps, but may not be enough to make good draft by itself.