Icy ruts are one of the banes of winter cycling IMO. You need studs on the front to "climb out of them" or otherwise allow your tire to keep tracking straight without following the rut where it goes. I am also of the opinion that your back tire needs studs for the same reason. On the one hand, if your rear tire finds the same rut as the front tire successfully got over your rear tire will sit in there and move your bike out from under you. On the other hand, your rear tire might not find the rut your front found, but might find another ending up with the same result. The best way that I can describe the sensation is a hand reaching up from under the road and pulling my tire hard in one direction.
If you do not have the side studs to grab the rut you need to turn your wheel hard in the direction you want the bike to go in order to get the studs you do have to contact the ice. Other than that - wheelies and bunny hops.