We are coming out of a rough winter - several nights of of hard freezes while we were out of town and unable to protect our plants. Our bottle palm is not looking well at all and I’m wondering if it’s done. The spear is very loose- I checked it the other day and it seems like I can pull it out. The push test on the trunk - it rocks a little bit - not as tight as in the past but still tight. Thoughts?

It doesn’t look good, bottles can take a bit of cold, but that looks frozen to me. 
If it  makes you feel any better i planted one yesterday, so all is not lost they will survive in cultivation. 
Such a shame it was a nice size one at that, if it has spear pull, then that is a pretty good sign it has suffered quite a bit of a substantial freeze. That cold blast even made the news in Australia! 

 

@BumGardener I'm pretty sure this one has a future in the mulch pile.  Unfortunate, but this cold snap was a little more than they can typically handle.

Agree with the above that it’s beyond help. All the ones I see around me are dead as well.

Echo the sentiment. Black spots everywhere. Pull it out and treat the soil with a fungicide. Later in the spring you can plant a bottle or spindle. I've seen them at Costco in the summer, cheap.

@BumGardener I most likely lost all 9 of my Bottles and Spindles at 22.5F with heavy wind, including a Spindle with 7 feet of trunk.  It looks like yours is probably dead too.  One thing you could do is "trunk cut" the top section to see if the new spears are alive or not.  This is just cutting horizontally down a few inches at a time to see if you can find clean tissue.  I am going to do this on a couple of Bottles in the next day or two.  It's the "last ditch effort" to see if there's anything alive down there.

So you can cut across with a loppers or a fine tooth saw (or drywall saw, etc) and look for clean white tissue.  Here's a good thread with photos of the initial cuts and how far down he went to find clean white tissue:

 

This is so depressing, I feel for my 9b/9a Floridians. You could replace it with Phoenix roebellinis. I have a similar pool style and they look very good and are pretty cold hardy.  The trunk isn’t as smooth or elegant as the more tropical palms, but the fronds look very tropical IMO.