Hey mate, Kyung Ah (Naomi on KOTR) and I did that exact hike in Winter a year back (or maybe 2 I forget now...), except in reverse. We started at Hwaeomsa and took off up through the bamboo thickets there to Nogodan shelter (there is a road to Nogodan, but it was blocked by snow so we left our car in a car park near Hwseomsa temple and started there). The ridge is not difficult usually and the snow from Nogodan onwards actually made the going a bit more pleasant. Hike times were very little different from any other season. We generally started a days hike at 4.30am more to avoid the crowds (and there still were small crowds) and there is a real magic to the hike through snow covered trails (occaisionaly mid-thigh deep, but usually only ankle) under the plop-plopping canopy of pine and fir at those early hours. Your headlamp lights up a small insular world and if the skies are clear, the stars are so bright. Definitely an awesome trip. But note: The ridge is very exposed to wind in certain places especially near the top. We saw thermometers in the shelter verhandah reading MINUS 20C. The wind was so strong at times we struggled to stay upright and I grew icicles on my eyebrows and my eyes stuck together. This was so much fun though, real adventure hiking in relative safety. Advice: Take the walking crampons (Eisen). They are 100% necessary. Trekking poles are also a great idea, one is OK two each way better. Gaiters (el-cheapo type perfect) and warm leather hiking boots really help too. A face mask (buff, balaclava, ski mask etc) saved the day too when wind-born snow ripped across our cheeks etc. Good warm gloves are also needed, though heavy jackets or down are not. When hiking your body is plenty warm enough, and when you stop, you should be at a shelter (heated enough in the sleeping rooms but cold elsewhere). A plastic bottle of pick-me-up (soju, rum, bokbunjaju etc) is also a great little addition to keeping the esprit de corps going strong.
Sounds like you'll have a great time. Might join in depending on dates and so on.
quem deus perdere vult, primus dementat