The Smokies are open (never officially closed), although many of the roads around the park have been closed due to snow and rock slides over the past month. That may be some of the source of the rumors flying around.
Snow conditions in the park.... No snow until you get to approximately 5000 ft elevation. Snow is currently at Rocky Top/Thunderhead (about 2 ft) and from Double Spring Shelter to TriCorner Shelter (up to 3 ft). The snow is melting fast with all the warm weather and rain. Most of it should be melted by next week, except in places that are well shaded.
I-40 - Hot Springs has no snow. I was in that area doing trail maintenance this past week. Snowbird, Max Patch, and Walnut Mtn (the 3 highest peaks in that section) are all clear of snow. There are a LOT of blowdowns in that area though. Some of the worst Ive seen in the southern sections Ive been on. I-40 to Snowbird has over 100 large trees down. I talked to southbound hikers that stated it was like that all the way to Hot Springs. I havent walked that section to confirm, but wouldnt be suprised.