Many times, the best solution is to not cross the river in the circumstances you envisioned. For anyone who has done river crossings, has the experience and knowledge to seek out alternative locations that are much safer and easier. Case in point with a couple of my photos below which depict a river (in summer) but the same circumstances can apply in winter.

This first photo shows a river that is glacier fed (cold) not that wide but is flowing fast and dangerous. As you can see by the terrain and environment, there is nothing to aid you in making it across that river safely. You could try swimming it across and as you get swept downstream, you may be fortunate to reach the other side before the river heads further downhill and consequently gets more dangerous.



This second photo was taken ~ 1 mile upstream from the above photo. As you can see, the river flows through many small channels and is easily crossed here....even in high water. Many times people get too fixated on their immediate situation/area and do not stop to think and also look at their map (you do carry a map right?) for much easier and safer locations.