Wait until early spring, around March 15, to assess the extent of the damage. Pruning too soon can be dangerous. If temperatures fall below 25 degrees Fahrenheit again, the newly-pruned cactus tissue will be even more sensitive to damage. If you leave it in place, however, it will protect the cactus from further damage. The growing spring tissue will respond better to pruning cuts.
Wipe down the blade of a sharp kitchen knife with an alcohol-moistened rag.
Inspect all of your totem pole cacti's stems for damage. Frost-damaged cactus tissue turns from green to purple or black. Cut away only the black cactus tissue. Black tissue is dead tissue. If left in place, it will slowly rot and take the healthy cactus tissue with it. Don't leave even thin margins of black cactus tissue behind.
Keep an eye on all purple cactus tissue, but do not prune it. It is damaged but not necessarily dead. It may bounce back to a healthy green. If it turns black, however, prune it promptly.