Hi again, Jason,
Yes, ice axe definitely. Also consult with Pinkham Notch about conditions… Sure you will know to do that.
What drives my clothing choices is my own experience biking and cross-country skiing in the winter. I know that I put out a lot of heat, and even in single digits biking all I need is a baselayer or two and a non-laminated softshell. More layers and I overheat fast. Any shell approaching windproofness and I overheat even with a thing baselayer.
Regarding my choice of non-laminated soft-shell tops and bottoms over waterproofs is twofold. On the one hand, any laminate is going to hinder breathability and lead me to overheat or be uncomfortable. Same thing with ski pants. While there are models with zippers you can start opening for venting, at that point you lose the wind resistance on exposed areas. If the ski or hiking pants have their own insulation, then they take away my ability to layer according to conditions. I don’t use any type of insulated pants for moving in any conditions.
Lack of breathability is also the reason why I don’t choose the lighter 2-5 oz windshirts, as I find most of them not breathable enough for me. I heard that older Houdini’s were very breathable, but they changed the fabric and they are not longer so breathable… Will they work, probably.
Second, my choice in purchasing waterproofs that are light is that they spend more time in the pack than they do on me, so I buy ligher stuff. A misstep wearing crampons will ruin the waterproofs fast (perhaps easy to patch depending on damage?). My winter softshell pants are a bit heavier fabric than the lighter season stuff. I could see a point causing a small tear or rip, but not a catastrophic one perhaps.
My pants are not OR Ferrosi. They are some EMS model from a few years ago. With roomie fit to accommodate winter weight baselayers but not superbaggy. My blue softshell top in the first picture is an OR Windwhirl and in the second picture below is the OR Ferrosi, of which you can see the red hoody sticking out.

What do I do to insulate my legs? On my first and perhaps second climbs, I bought a pair of baggy military fleece pants that came with side zippers off of eBay for short money. They have a baggy fit that makes them easy to layer over the softshells. And then an old pair of full zippered waterproof pants. So I guess I did wear my waterproof bottoms after all… Those fleece pants are bulky to pack. I found the leg insulation was plenty, so I dialed it back to lighter weight, fuzzy fleece, pajama style. But I found my gaiters provided enough wind shielding and that to be enough for me to hang around for about 30 minutes at the summit. So the fleece and waterproof started staying in the pack. If we were to stay longer, I would need to don the fleece and extra shell. I bring a Jetboil Joule and I always cooked a dehydrated meal up there. See picture below:

And finally, I apologize if I sound like I am telling you not to bring waterproofs… In my first two or three ascents I brought a heavier, three layer setup (Goretex bottom eVent top). After that, I reevaluated them and see them as a low chance of use. Certainly not while moving, so breathability is not needed. I substituted them for silnylong waterproofs… Much lighter and less bulky. What I meant to say is that I just do not think you should overthink them too much regarding the best technology, as opposed to trekking in the rain at 40 degrees. If you use them, chances are you will be static, so breathability doesn’t need to be great. Durable waterproofing doesn’t need to be either, as any shell, including softshells, are enough to fend of a snow storm for a couple of hours. I would only pay attention to them if I expected wet snow, which in January will probably be unlikely. If someone were buying a top of bottom for this trek, I would say to get the least expensive they can find.
Ultimately, your own body determines your choices. The buddy that I have done most of my winter outings with will at times trek for extended periods wearing his superwarm Rab down puffy–much warmer than the one I am wearing in the above picture. I sweat just looking at him while wearing my baselayer and softshell top. So reflect on your active winter experience. What do you need when cross country skiing, biking, running, high pace snowshoeing…? That will determine what you need while moving up Mt. Washington.
Packing lists… Gloves, gloves, gloves. thing ones, thicker ones, mitts that layer over… Fit is key. Make sure they don’t constrict your circulation when. A cheap pair of work gloves from the hardware store will give you enough dexterity for basic tasks (like adding and removing crampons) and their low price won’t make you flinch when you snag them.
Also, fogging ski goggles can be a pain. There are some Smith models that come with fans… Nice to have, but not needed. I am sure other manufacturers followed suit… Haven’t had to buy in a few years…
Lastly, the only person I have seen get in trouble at Mt. Washington first hand is the guy in that second picture. My friend invited him to tag along with us. I had some concerns, but my friend vouched for his athleticism and they are very close friends. The tag-along being a doctor, I figured he would understand his own biology with regards to water and food intake, hypothermia, etc. He started great, but as it turns out he was feeling progressively worse all the way up. He did not say anything to his friend or me. He did not have any first hand experience in the winter. He ignored our snack and water breaks. When we asked why he wasn’t eating or drinking, he just said he wasn’t hungry or thirsty. Since we had highlighted the importance of hydration and food, we assumed he had been taking care of himself while trekking and we did not notice it. I did notice that he slowed down after Lake of the Clouds more and more to almost a crawl, but we thought he was just tired and he said he would be slow but wanted to make it to the top when we asked. Eventually got to the top, took the pictures, ate a dehydrated meal, and headed down. He was flying down the mountain. Much reenergized. In the car on the way home, he was telling us how he thought he was going to die on the way up and that the food on top brought him back to life, which I had turned to soup by adding extra water. That he had been feeling terrible but did not want to ruin our trek. In asking how much he had been drinking it turned out that he had not touched the water in his backpack at all. That buffled me. All he had had for a drink all day was a coffee when he had had when he got up at 3 a.m. So he obviously had been suffering from severe dehydration accentuated by the coffee he had had earlier.
My takeaway is to make sure all members of the party understand that safety comes before any objective. Make sure to have all member monitor their body for discomfort regarding low blood sugar, dehydration (lots of water in winter) and hypothermia. And to have them speak early when small issues can be easily managed. I probably should have taken a more active approach in doing more proving checks on this person, rather than rely on the person’s athleticism, medical knowledge and my friend to check on him because of their friendship. And he was walking really slow, I should have realized that something was wrong and turned back despite how close we were and his insistance on finishing.