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Is there anything between the plant and the plastic? I have seen plastic do more harm than good for palms from what I've seen. It doesn't retain any heat but it does retain any moisture that gets under it (and any moisture that evaporates inside of it).
If there is burlap or something under the plastic, I think that will be good enough though.

Good luck!
-Alex

Sorry, but that looks like a recipe for disaster. Plastic is just asking for problems as Alex said. Why not just bring it inside for this event.

The leaves can recover from freeze damage, and the palm can regenerate as long as the meristem survives. But if the roots freeze, the plant is toast. Because the roots have so little protection from surrounding soil, plants in pots generally lose at least a full zone of hardiness over the same plant growing in the ground. Heck, I'm worried about a couple of ginkgos I have growing in pots.

Plastic doesn't breathe. So you may want to use Burlap with a plastic bag over it to keep out the rain/snow. You SHOULD wrap the sides of the pot in attic insulation and add mulch to the top of the dirt. This will give you the best chance of not seeing the dirt inside the pot freeze.

Low temps will be down to the low teens over the next few days.

If it's potted, why didn't you bring it in? With these temps, the roots are more likely to be permanently damaged in a pot.

I agree potted plants are always very vulnerable in this weather. Pots can freeze solid with temperatures only in the 20s while the soil in the ground may only be frozen an inch or 2. I don't think trachycarpus in the ground will ever have their roots completely frozen in our zone, but in a pot it is very possible without protecting the pot as well as the entire plant from the cold.
Bringing it in is definitely easier since this is going to be a very long term freeze. We may go 10 days or more without getting above freezing in the next few days with several nights in the single digits. This is definitely the worst winter for plants in the area in a good 20 years and maybe more depending on how February pans out. It's a real test for marginal plants like trachys.

Good luck!
-Alex