As someone who does and has taught ice rescue I'll help Tom out a bit here with his dislike of river ice.
There are many reasons river ice is less safe than say pond or lake ice as a general rule river ice is considered at least 15% weaker than say lake ice. I'll hit on some of the major reasons that should give you and idea of what to look at and think about.
River water is generally in motion all the time even if it's a very low flow. So currents working under the ice can make it unpredicable from day to day as it wears on the ice sheet unseen. Rivers levels tend to go up and down with tempurature changes as melt water flows in or stops flowing in. This can leave the ice sheet floating with open water or soft ice at the edges along the bank. Or as the water drops the ice sheet can become suspended along shore around beaver lodges or other obstructions. Ice gets a great deal of it's strength from the water it floats on supporting it. Not only is it very dangerous to walk on ice where the water has dropped leaving it suspended. It can be impossible to get out on you own once you've fallen threw and difficult or impossible for even a rescuer to assist you getting out. River ice tends to be stronger on straight aways and weaker on curves again because of current. Current can stack ice up creating pack ice which can be very unstable and dangerous to walk on or cross. Ice on rivers is often subject to what is called over flow where water runs on top of the ice. Anytime you have water on top of ice it is degrading the ice and making it soft. Just like ice in your drink glass water degrades ice because it's warmer.
There you go..
These are just some of the many factors that make river ice less safe to be on. I know I can list more but for the sake of not writting a book or sounding like a preacher,,, I'll leave it at the very high points.
Now all that said I still travel on river ice myself. But I pay close attention to the condition I'm dealing with and usually I wear a float coat. I don't just wander around without sounding the ice with a spud bar or looking at the big picture.
Good luck and be safe.
Mac