You could try a surface coating but cover the whole thing if you do or it won't look right. It also won't last long and may not make it through the next winter. It won't match the rest of concrete around. You never know how long it will last so I wouldn't recommend doing it. If you have a contractor bid it out, then ask for a similar job to look at first. You could pour another couple of inches of concrete but that won't last and won't work on the sidewalk.
It boils down to an economic decision and aesthetics decision like all the others. Price the surface patch and total replacement and compare it to your budget. Then compare the looks of the different options.
I assume you know not to use deicer on it now although I use the potassium chloride stuff (instead of the calcium chloride) occasionally without any problem. You need to sweep it off after the ice is gone. Some road departments around here quit using it on bridges for that reason even though the bridges needed deicing the most. There is some new liquid stuff now but they went to either straight sand or a sand/ice mix before the liquid.
Sometimes the concrete mix, its additives, and/or especially the finishing procedure makes a difference. Talk to the concrete company about any recommended mixes in your area.