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.
Well put - wasn't this exactly the mistake that Chris McCandless (Into The Wild) made? He could have hiked upstream a short way and found a reasonable crossing, instead he retreated to his bus and his subsequent demise.
I recall that from the movie and depending on many variables, sometimes it is better to head upstream or head downstream where the lay of the land may level out and provide a safer location to cross, thusly enhancing your odds of living another day.
For example, in the photos I posted, the river eventually slows, narrows and shallows significantly (knee deep in winter) a few miles downstream on relatively easy hiking terrain at which time, a winter crossing of the river is a very viable option...Albeit there is always still some risk involved.
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Earth and sky, woods and fields, lakes and rivers, the mountain and the sea, are excellent schoolmasters, and teach some of us more than we can ever learn from books.
John Lubbock