What you've got is probably mites. Take the plant back outside and wash it
off with a garden hose. Then make up a soap solution using real soap not
dish detergent and add to it a cup of garlic powder. Use a sponge and wash
the remaining bugs off the fronds and trunk. This is not a permanent
solution to the problem and will probably have to be repeated once or twice
while the palm is indoors. The rain washes mites off the palm while it's
outdoors and there's, hopefully, no rain in your house.

Dust some of the white spots onto dark paper. If they move, they are
insect or mites. If it is too cold outside, try putting the palm in
the shower inside the house to wash it. Water temperature can be
regulated as well as the temperature of the room.