PlantLife Online

Answer

With an altitude above 6000 feet I am assuming you receive subzero temperatures throughout the winter, this will make it nearly impossible to successfully grow a palm tree. The majority of palms come from the tropics however there are some which are native to areas that receive some snowfall. The problem is that in areas with freezing temperatures the ground may also freeze, the tender roots of a palm will not survive such conditions. There are several varieties which will with stand some dips into the low temperatures however long periods of time below freezing will be difficult to overcome. Here is a list of the best palm trees suited for the cold. 

• Phoenix dactylifera Date Palm - (Cold hardy to 20 degrees)
• Phoenix canariensis Canary Island Date Palm - (Cold hardy to 18 degrees)
• Sabal texana, mexicana Texas Sable Palm- (Cold hardy to 18 degrees)
• Chamaerops humilis Mediterranean Fan Palm - (Cold hardy to 5 - 15 degrees)
• Washingtonia filifera California Fan Palm- (Cold hardy to 15 degrees)

• Washingtonia robusta Mexican Fan Palm- (Cold hardy to 18 degrees)

• Trachycarpus fortunei Windmill Palm- (Cold hardy to 5 degrees)
• Butia capitata Pindo Palm - (Cold hardy to 15 degrees)
• Cycas revoluta Sago Palm- (Cold hardy to 20 degrees)

Keep in mind these are absolute extremes any long term exposure to these condition will affect the health of the palm tree.