It's extremely rare to see a shelter closed this time of the year. For the most part, shelter closures occur in the summer/fall due to bear issues. Getting to Newfound Gap is the only thing that can slow you down. They close 411 for pretty much any kind of snow.
I highly recommend waterproof gaiters if there is more than a few inches of snow, but that is just me.
Looks like lots of snow is up there now, but it usually melts very fast.
I was up there 2 years ago and it was -3 at Pecks. I awoke to 6 inches of snow. Be prepared. Pecks is an ambitious day hike with the short days, lots of snow, and a late start.
Just going to the Sawteeth might be a better idea. If you think you can make it to Pecks though, go for it! Best privy ever.
Let me know if you want other route suggestions. GSMNP is great in the winter time, especially if you time it with snow.