If you are looking for some place to go and see trumpeter swans right now, I can give you a few pointers. First, look for open water. As cold as it has been, that largely means rivers, as almost all still waterbodies are locked in ice.
The South Fork of the Snake might be the closest place to Idaho Falls with significant swan activity. I found swans on either side of the Heise bridge and up as far as the road closure. Incidentally, the road is closed at the Stinking Springs parking area this year. I don’t know the reason but I suspect the deep snow may be the answer.
Swan Valley may no longer be home to summer swans but in the winter time can re-earn its name. Trumpeter swans appreciate that the South Fork will have open water even when temperatures stubbornly resist climbing above single digits for day time highs. You can find swans from the bridge across the river upstream. I drove up the river road on the Fall Creek side and saw several dozen. I was even treated to a scene of white-tailed deer and swans together. I have never seen that before.
Rainey Creek also has swans, especially once you start up Highway 31, at reasonable distances. Like all swans, they are a little jumpy though. Stay in your car and they are more likely to stick around.
The Henrys Fork in Island Park also has a lot of swans right now. The river is frozen through Harriman State Park but you can find swans at Last Chance and Mack’s Inn. At Last Chance, you will likely have to wait until afternoon for the fog to burn off so try Mack’s Inn first. You can drive down toward the North Fork Club entrance by turning into Cafe Sabor on the north side of the river and following the road. This is a narrow road though and you may have to back up if you meet someone. There are a few driveways that are plowed out that you can pull into to let someone get by but obviously, you can’t park there. There is a big turnaround plowed out at the North Fork Club gate.
If you want to see massive amounts of swans, head to Deer Parks. My friend, Paul Faulkner, manages Deer Parks and he reports that there are about 2,500 there right now. Watch for them in the fields south and west of the headquarters buildings. You can view these from the road or walk in toward the shop area for a little closer look. However, as the swans leave to go to roost for the evening, they might fly right over you on the road.
If you have never been to Deer Parks there are two ways to get there. From Idaho Falls, it is often easiest to take either Lewsiville Highway or Hitt Road and go north to Menan. At Menan, turn east. At the substation, turn left (there is a yellow house on the corner) and just follow the road until you end up between the two Menan buttes. Deer Parks is on the west side of the road.
You can also take Highway 33 west from Rexburg. Once you pass by Beaver Dick Park, take the next paved left (it is across from the gun range on the north side of the highway). You will pass the Madison County Landfill on the east side of the road. Take the next right turn and follow it. You will pass the trailhead to the top of the north Menan Butte and you will see the Deer Parks headquarters on your right, or west side of the road.