She must have walked that route hundreds of times. It's always possible to slip but I would expect to find some sign on the riverbank where she may have fallen and slid into the river. It has been extremely cold recently so the water temperature may only be around 4 or 5 Celsius meaning she would have had to leave the water immediately to avoid cardiac arrest. I hope there is another explanation and she is found safe and well but the circumstances of her disappearance are very worrying.
I have a rather insane relative who lives up in Yorkshire and is fond of a good invigorating river swim even at this time of year. While I'm sure she has acclimatized to it. I can't imagine it's cold enough to be quite that deadly if she takes regular dips in January/February times. The old witch is near 80 so it must be doing her some good, though I'll happily shave a few years of the top to avoid that bit of healthful exercise.
NB was wearing slip on wellies, so at the least she should have been able to slip out of them if she was in the water or somehow stuck in the mud. But likely was wearing a thick coat/hat scarf etc which would weighing her down.
I suppose that is a question not answered -
can she swim? And if she can, does she swim recreationally/is she a strong swimmer?
Though maybe knowing isn't that much help.
If she can't swim- she isn't likely to get into a fast moving river (unless her dog looks about to drown.) She might try wading out a bit if she had knee high wellies though and slip - no marks on the river bank that way and she'd be less likely to strip other clothes off before going in.
If she can swim, she might have thought she could get to the dog but underestimated the river, as many casual pool swimmers do.
If she straight fell in, (trying to get the dog out of just by accident,) fully clothed she might have a lot of trouble getting out again swimmer or not.