I have successfully overwintered palms in temperatures of -37* in a heated shelter. I am still altering the shelter structure to create a better winter environment. Last winter the heating cost was $80~. The shelter kept the interior temperature above -5*C/23*F. A European fan palm (Chamaerops humulis) came through the experience with little damage while a Jelly palm (butia capitata) sustained about 30% frond damage primarily due to sunburn in the spring and insufficient soil moisture.
For zone 5 or 6 I would recommend Sabal minor. Plant it about 2' from a south facing wall(preferably stucco or brick) of a heated building. Use 1" styrofoam board to insulate the soil by creating a 3 sided box that extends from the building's foundation and surrounds the palm's root ball. the box should be level with the soil surface and extend 1' deep into the soil. For the winter build a 3 sided box that will just contain the leaves. Use 1" styrofoam board to insulate the box and paint the interior of the box a flat dark color to provide passive solar heat. Secure the box to the ground and make sure that the sides form a windproof seal with the building(foam rubber works well without marking the wall). Leave the top of the box open as long as outside temperatures are above -10*F. When temperatures are forecast to go below -10*F put an insulated top on the box until temperatures recover. The inside of the box top should be painted a highly reflective color to reflect the heat back into the box. When the box is removed in spring cover the palm with a sunscreen to allow it to adjust to increased light.
Try
Palms in Colorado Springs (USDA Zone 5b)
These people have been experimenting with overwintering palms in zone 5b.
If you want to try something easy and cheap use a Livistona chinensis (Chinese fan palm) instead. It is a cheap palm found in most box stores tropical plant sections. Instead of building a winter box, mulch heavily. The leaves will die back to the ground but the palm should regrow from the roots. It worked in Ontario in zone 5a, but not for me in zone 3a.
If you want to try something expensive and time consuming, contact me.
Most of the people growing palms in Zone 7 and colder are experimenting and learning from their and others mistakes.
Allen