Bring Chains, and check the WSDOT site. I believe if it gets to bad the road will close, but it doesn't happen all that often. Wrath will have a better answer, but he might be sleeping by now so he can get up to get the goods tomorrow.
I'm awake...working nights and also got to work in the afternoon....but per report from the daughter, yesterday tues...waist to chest fluffy.
As for the road...
Early morning dumps...Glacier to the hill...before 6-630 am you will likely be on your own...very few cars and the plow will perhaps have been through once. Best hitting Glacier at 730-8 the non-very-early employees are driving up and just follow them. The big line up is between 830-930...which is not usually bad, it just is.
Bring chains, shovel and blanket, get in cue...(btw...really no reason to pass 1-2 cars because there is a line and you will pull into the parking lot....5 seconds sooner. And the risk spinning out or going in the ditch for 5 seconds). On gaper tourist days when there's lot of snow or it's slick you will see tourist, the non experienced or hotrodders in the ditch...last Saturday there were 5-6 of them. If a car/truck is doing the slow steady conservitive cruise (that don't use their brakes...no brake lights constantly going on/off) its a local who knows were the hazzards are...just follow them and you'll get there. I've chained up 3-4 times in 10 years with a rear wheel drive volvo wagon and only ended up in a snow bank once (no chains) going down...but I consider myself an experienced snow/ice driver.
DOT keeps the roads fairly drivable...meaning less than 4-6 inches of snow...but it can be packed, slush, ice, greasy or wet. Dot only closes the road due to a slide or very high avy danger. Though very early am or late night...idk 9pm to 5am they don't plow much...so it can get too deep to drive. Going up....leave enough room to keep rolling, don't stop. Going down...leave enough room to stop, try not to use your brakes, just be in a lower gear...lots of folks slide off in to the trees or a bank when breaking for a curve.
If you need to chain up do it at the plow shed or there is a couple of places on the straight aways before that are flat with alot of room and after the DOT shed there are a couple of pull outs on the curve...though some times it tough to get going because of the line of cars and a slight incline. A half mile after the DOT plow shed is when you start to climb.
There are 3 hairpins, the third one is the deal breaker...if you barely make the first hair pin...chain up for the third one. The 3rd one is a very sharp right that is on an incline and if you stop or can't make it...you will FU*&^*&&%$% up the line. You have to be going...rolling enough to make it around and up...you don't want to lose traction and start spinning the wheels...yet be going slow enough to not slide or drift into the other lane...you can't see the traffic in the on comming lane nor have to break and lose your momentum and get stuck spinning.
If it is puking and dark...early mornings or eve...visability can be a real issue, especially if you don't know the road and where to keep your momentum or where to slow down to make the curves/turns.