yeah I highly doubt it's your tires. Has to be an ABS system malfunction. The only time an ABS system kicks in, is when one of the sensors detects one wheel is slowing down faster than the rest of them. For example, if your foot is on the brakes, and a single tire slides in water or ice, the abs kicks in to let hydraulic pressure out of that wheel's brake line. This would, in theory, keep the tire from sliding, and help keep the vehicle under control.
Your tires aren't the issue if your ABS is coming on when it isn't supposed to, and you aren't sliding.