At first, I want to say it is a warped brake rotor, but you would feel that all the time when braking. Based on your original description, it sounds to me like the ABS is actuating.
To be honest, the most common cause of this type of condition is related to a wheel speed sensor that is failing. Now, if you told me it never does it on dry roads, I would say the ABS is working properly.
What you can do is check each of the wheel speed sensors. It is a little time consuming and requires a little knowledge of using a digital multi meter. Here is a link that explains how to do it. I will add a few extra links below to help with the process.
I attached two pics below indicating sensor location. Pic 1 is front and there is one on both sides of the vehicle and pic 2 is the rear.
Let me know if this helps or if you have other questions.
Images (Click to enlarge)
Friday, January 24th, 2020 AT 9:28 PM