rockm

"It is the desert so snow is rare. I know the evergreens don't mind low temps but will the roots freeze being in shallow pots?"

Shouldn't make much difference for the species you've mentioned, possibly the Chinese elm, depending on the cultivar. A sheltered spot outside outof the wind, under six or seven inches of mulch will probably get all these throught the winter. Trees can take frozen roots--happens all the time in nature. The vast majority of a tree's roots are in the top six or eight inches of soil--above the frost line.

The trick is to shelter bonsai roots from EXTREME, prolonged freezes below 25 F--With mulch, you trap "warmth" (a relative term) that the ground accumulates during the day. The mulch prevent sudden big drops, or increases --which can also be problematic--in soil temperatures. Those temps tend to stay 5-10 degrees warmer than air temperatures. Dont' worry about teens at night, as under mulch, the inner roots of the tree aren't that cold...