Can melting ice be done stylishly or done with Command Blocks?

Solution 1:

Well, you have a couple options..

Option 1

Change the biome, using a tool like MCedit. Any biome that isn't "cold" or "mountainous" will melt ice.
The "Mountain+" or "Hills+" biomes only melt ice above a specific y+ level, which leads us to the second Option, if needed.

Option 2

Lower the river's elevation. In "Extreme Hills", snow forms and water freezes at and above y+92. If your river is below this, no more ice forms!

Option 3

Use /gamerule. /Gamerule randomTickSpeed 0 will prevent ice from forming.
However, because of the effects of randomTickSpeed, the result will additionally affect other things. If this gamerule is set to 0, leaves will not decay, crops won't grow, grass won't spread and more.

Option 4

Use a Plugin, like Worldguard to disable water freezing in a certain area.

Option 5

High-intensity Light should prevent ice from forming.
Any block of water with light source of more than 11 will not form ice, but this is hard to do underwater because water decreases light-spread twice as fast as air.
Example: light travelling one block in air goes from 15-14, but in water it goes 15-13.
If your river is more than a few blocks wide and you don't want to put lights nearly every other block permanently underneath it, this may not work for you.

Option 6

Finally, you could just have a repeating command block that constantly does a fill command replacing ice with water. fill X Y Z X2 Y2 Z2 minecraft:water -1 replace minecraft:ice.