I believe it is only 1 possibility but...On each wheel is a speed sensor and cable, the cable has a plug and socket if memory serves, you may choose to take of each wheeel and look for the speed sensor cable and check for damage and undo and re do the plug, squirt a bit of Wd 40 etc for good measure, not hoigh chance of sucess but zero cost. I had a similar issue when it rained, once Diagnosed it was a sensor fault and on inspection found the insulation on one cable was "cracked", new speed sensor ( came with relevant cable as one , of course, sorted issue.
NOTE as one of the guys mentioned it could be a wheel bearing on the way out, the play in the bearing would cause mos alignment of the sensor and so fault... as knackered bearing will get costly if allowed to go on give each wheel a wiggle when jacked up to check it isn't this. ( I think bearing would hav eto be well buggered to cause that much play and you would hear it, but... Cheers Michael