The tundra is primarily always frozen. As you point out freeze/thaw cycles are terrible for biochemical stability, but at the tundra below the surface (where earth acts as an heat insulator) I believe this effect is minimized

DNA has some remarkable stability properties when it comes to preservation. This is one of the reasons people are so interested in DNA storage technologies.

DNA chemistry allows for information to be preserved for millenia at sub-zero centigrade temperatures.

Robert N. Grass, Reinhard Heckel, Michela Puddu, Daniela Paunescu, Wendelin J. Stark. Robust Chemical Preservation of Digital Information on DNA in Silica with Error-Correcting Codes. Angewandte Chemie International Edition, 2015; DOI: 10.1002/anie.201411378

It depends of the species, but polyploidy is common in plants because plants often can work as colonial organisms that can clone itselves.

Is the same problem as to restore a file that is partially distroyed in four or five points. You can still recover the original file if you have five copies, each one with the damage in a different area. Polyploid organisms have several identical security copies of each chromosome. If something in a chromosome is damaged, they can quickly fix the damaged areas using the safety copy saved in his 'twin' chromosome.