Cannot remove saddle from my dead horse remotely

While exploring New Hanover I had a horse die in the same way yours did - a fall into a river. When your horse dies in water it cannot be revived and the saddle cannot be retrieved. Unfortunately, water-related injuries are a death sentence for your horse.

Since your temporary horse is out of range you must either find a way back to civilization, steal an owned horse or tame a wild horse. No matter what, you'll be doing a bit of walking.

As you noticed, the saddle icon will appear on your radar. In this situation it cannot be interacted with. Your two options are to load a saved game to a point before your horse died or visit a stable and select a primary horse from there. When leaving the stable the horse should automatically have a saddle. You will also have the option equipping other saddles while you're at the stables if you desire.

Were your horse to be injured on land you would have been able to revive it, or mercy kill it and remove the saddle.

I was roaming with my horse where we fall down a cliff to river, the horse died and drowned. The body is in the middle of river. Now I cannot remove the saddle.

The saddle is not something that is removable while the horse is in water. It's equipped to the particular horse, but if you took your current horse to a stable you could reassign the same saddle to another horse.

Also There is only the saddle icon on the radar.

The saddle icon on the radar is telling you where your main/currently "equipped" horse is.

What should I do?

You can use horse reviver on the horse to get them back up, they're not permanently gone yet. If you don't have any I suggest running over to a stable or general store to grab some. (This is unavailable when a horse has died in water as mentioned)