In Unreal Engine five you can use the Linear Velocity mode and ad Random Range Vector to its Velocity varible. In there you should set the X and Y to -1 in minimum and 1 in maximum. Also if you set the Z value to 0 for both of them it won’t add vertical velocity to them.
Since this solution applies the velocity at the spawn of the particle. It won’t affect the gravity. You can also apply the same strategy in Unreal Engine 4.