Put Down those Clippers!

Pruned Basil that is now wiped out from recent low temps.

Ok, so the 3 nights of "below 32F" temperatures have passed here in Arizona (Dec 30th, 31st, and January 1st nights), and maybe your plants are as damaged as mine despite your best efforts to preserve them, but DO NOT prune back the damaged plants yet! 

Wait until
- all the danger of another frost is past (Spring)
- the damage to each plant is clearly 'sealed off' by the remaining living plant, and new growth is visible beneath or adjacent to the existing damage
Yes, the damage may be ugly, and it might bother you (as it does me), but every reliable bit of horticultural advice I've read (here, here, here, and here) clearly says to wait to prune.  Pruning re-opens wounds and makes plants more vulnerable to further damage.  Pruning also stimulates growth hormone in plants, and drives them to put out new shoots which can be severely damaged if the weather gets cold again.

Previously glorious Honeysuckle

Also, I noticed, the plant damage in my backyard was relatively minor on the mornings of the 31st and 1st, when the dew points were down in the teens. But on the morning of the 2nd, when the night time temperatures were HIGHER than they were on the previous 2 nights, the damage was MORE severe.  My theory on this, is that it is NOT the temperature variable alone that matters, but rather the temperature combined with the relative humidity (the dew point).
--------- min Temp --- Dew Point
Dec 30th     38                27  
Dec 31st     32                17
Jan 1st        30                16
Jan 2nd       32                22 (minor frost seen on walls and leaves)
Jan 5th        37                34 (actual frost seen on street parked car wind shields)

As the Dew Point increased, and the ambient temperature decreased (see the graphs at each link above, on the green and red lines) the propensity for FROST increased.  Dec 30th and 31st were colder, but there was no actual deadly-to-plants ice crystals visible on the foliage.  January 1st, you could see small amounts of white frost on the cinder block border walls, and tiny flecks of white on some leaves, prior to the sun melting them.  January 2nd morning, the plant damage was not just decimation (one out of ten) but much more widespread.  So it ain't the dry bulb temperature, it's the wet bulb temperature, the dew point, that really matters here in the desert in the winter, combined with a cold ambient.  Take the moisture out of the air, and the plant won't be attacked from the outside.  Lower the temperature enough to crystallize the water internal to the plant's structure, and you can rupture the rigid cell walls from the inside-out, but this takes longer to do than external ice formation..

Some aloe froze, others adjacent did not.

Hibiscus is 90% lost.

New Lemon shoots, burnt by frost

Protecting the aloe flowers didn't matter.

Lantana is 95% lost