If its a spider, than its a good thing. They will eat alot of bugs that are bad. But what you need to watch out for are spider mites. That doesnt look like spider mites though. If you tree has spider mights you would see webs under the fronds and the mites are so small you can barely see them. There will be tons of them and usually the fronds will start to turn colors. Misting or spraying off the fronds and stems are a good way to get rid of them if you come across them in winter. They like dry conditions.
Hope this helps a little. Good luck :)

- US_Marine

They are spiders which are of no threat to your plants. Like US marine said, spider mites are a problem (and they love majesty palms when they go indoors). You wont have to worry about spider mites outside because rain and humidity takes care of them, but when the plants go inside for the winter, they come out of nowhere!