When traction is being lost, such as on snow, wet roads, gravel, etc., it is typical for the DSC light to flicker. That is not important. The lights remaining on at all times is out of the ordinary; I had a similar experience last year, throughout the winter and rain, after the DSC light started flickering. Similar to what Johnny mentioned, it might be a mechanical problem with the sensor, ring, or sensor wire. However, it could also be the result of a software glitch in the control unit or a computer flaw that prevented the CAN from receiving data. Sometimes, computers do experience issues.
I would assume that this problem rarely happens because of a software bug in a unit connected to the CAN, because your ABS and DCS still function, just like they do on my car, even with the warning lights. 🤷♂️
My advice would be to wait it out and not replace anything until you've given it a good inspection. 😉