Foxtail Palms should weather the cold snap, but the only way to know for sure is to wait for a new frond to appear. If you don't get one in month, then you've probably lost the palms. Don't trim the dead fronds off of a self-cleaning palm. Wait for them to fall, regardless of how ugly they look. If you continually trim any self-cleaning palm (like the Foxtail) you will cause the crownshaft to thin and eventually kill or deform the palm. This is called "penciling" because it will start to look like a sharpened pencil.

i agree, i have a few just like that of what you described. if your temp. got pretty low this past winter it would be the cause of this! maybe below 25*F or so. mine got down to 20*F this past winter & a few in the pots had this but none in the ground! it should bounce back really quick with all the hot weather lately!

10C or 50F is not a chance for a Washingtonia. I went through that and gave up 7B/8A climates and long terms survival for any palms other than Trachys, Sabals and an occasional Butia. Even in zone 11 here they don't look at their best. My Washingtonia was killed at 14F just one night of 14F and one day of 30F was enough for all my Washies. In fact Wash. filifera is not doing well in a rainy climate or a semi-shade or both, I would not take a chance either in a rural area zone 8 with any of the Washies. 8 years experience talking. Now I am in a zone 11 without much heat, so it may not be a true zone 11 since the low temps March the 11B but high temps are never above 80F. Even the 80F is reached a couple days a year for short periods. I would say Washies are best for zone 9 and up, maybe marginal for 8B. That's it. Your Washie is dead or dying and even if it comes back, it will not last long. The next winter will kill it. It is now too weak to survive. Move to a warmer zone. I lost too much money playing with borderline zones. Get your plants one or half zone below yours and you will be safe.

The soil looks very dry. I am not sure where you are located, I live in south florida and the sun would not be an issue for a foxtail palm (assuming it has been in full sun at the nursery). I would possibly dig up the rootball (be sure not to disturb the roots) and dig a hole twice the size of the the rootball and work in some garden soil (be careful not to use too much). Then I would mulch the area to hold moisture and water regularly until the soil changes. Just and idea :) When you water, does the water absorb right away or does it just run?