Hopefully, right know your palm is getting plenty of sun. It has a chance of recovering since the spear has not pulled yet. I would not even think about operating right now. Some people spray their palms with copper fungicidal spray for cold damage. The best thing right now is to keep the crown dry and cover the palm again if the temps drop.

Wasingtonias dont give up their spears when dead as easily as other palms do so just because the spear doesnt pull doesnt necessarily mean it is still alive. It might be alive though, so just keep an eye on it and next time protect it before it completely browns (protect below 25F). You will have damaged fronds in the spring, but you should have green fronds too and the more green fronds that you have, the better!
I hope it makes it for you!
-Alex

Looks like it is still alive,I would leave it for now.

They can take a while(eps when small)to get going in spring.

As it gets larger,root protection will be every bit as important
as foliage.....lots of mulch!

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Thanks! Its my first attempt at a Washy. I know now to provide more protection earlier and later then for my Windmill, European Fan and Pindo. Those three have zero damage. Hopefully, it will pull thru. If not, its a lesson learned.

Update, I checked the crown closer and it appeared soft. So I got the saw out and cut. There was rot in the middle. Its nearly flush to the ground now, but the trunk is no longer soft. If it survives for some reason, I will post an update. At least the weather is ideal with highs in the low 80s.

Can you post a picture of how far you cut?

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Here is the Pic. Major Surgery. I had to go down this far to find solid material.