Yep, all of the 2-lane roads mentioned offer 2-way traffic
Assuming a Jackson, MT starting point, the only logical way to reach Salmon, ID in winter is MT 278 to Wisdom/MT 43 to Lost Trail Pass @ US 93, then the southbound descent to Salmon. Pass through Salmon to Challis on US 93 and at Challis take ID 75 through Stanley to approach Sun Valley from the north. There ARE routes through the Beaverhead Range along the MT-ID border/west wall of the Big Hole, but they're not passable by vehicle in winter.
Caveat: I've never driven ANY of this in winter. I have in fact never set foot in either MT or ID in winter. But I've spent some time daydreaming on dreary winter afternoons at my NC office while looking at live DOT webcams all over MT and ID. All of the route from Jackson, MT to Challis, ID is along major highways in the state and regional sense, and they're plowed early and often. I have a friend in Challis who regularly makes winter trips to Stanley for snowshoe hike-ins to remote hot springs and for snowmobiling, so I have an understanding that at least Challis to Stanley is well-maintained in winter. Stanley is a destination for snowmobiling and snowshoeing and likely for XC skiing, too, so I'd be surprised if its sole paved access along ID 75 from both directions is not heavily plowed in winter. It shouldn't be too difficult to get a feel for the whole thing with some communication directly with ID DOT and/or some daydreaming time on their webcams, some of which I'll bet are along ID 75.
You might be interested in seeing if Sharkey's Hot Springs above Tendoy, a little south of Salmon and just a few miles off of ID 28, is accessible when you're in the area. Sharkey's is a very nicely developed BLM facility, right on a graded gravel road, unmanned, with the hot spring waters piped into two large concrete tub/pools, with concrete aprons, changing houses, and bathrooms. You might see my Challis friend, Skndip on the Interwebs, there if it's accessible--he and his wife are C/O hot springs junkies and routinely spend long afternoons basking in the sunlight which bathes Sharkey's wide-open locale in winter. I would imagine a call to whatever BLM office includes Salmon or even a Salmon Forest Service office could confirm up to the date access to Sharkey's along Warm Springs Rd from ID 28. Warm Springs Rd ascends Lemhi Pass for crossing into MT west of Grant, but that's always closed in winter, to the best of my knowledge. Look Sharkey's up on the Interwebs--it's a very inviting spot.
Foy