Models are in agreement for clearing overnight into tomorrow. The problem is, initialization show them clearing as of now and by looking at the obs, they are still in the fog. But, looking out my door and at the various webcams in our network, the layer is slowly lifting like it usually does around sunset when drier air is working in. Looking at current water vapor maps, there still is plenty of low level moisture to work with although current vis sats show a clearing line just north of the Canadian border working down. So this puts the 850 RH maps about three to six hours too fast with a drying pattern. So, will there be clearing overnight, probably. Will the summits be clear at sunrise, maybe. When the sunrises tomorrow, it might be enough instability to generate a bit of summit fog for a few hours since the drier air is still a ways back and will be on the fringe of passing tomorrow morning. Wednesday would be a safer bet for sunrise but as Bill mentioned, melting will be a problem.
If you have been watching the cams, you might have noticed the frost line has slowly creeped up the side of the mountain from Saturday until today. This line will continue to make its way up since there are various factors working against keeping it. One is heat. Temperatures are expected to continue to climb for the next 36 hours, even overnight, to upper 40s and 50s by Friday. The summit does not have diurnal cycles, so warm days and cold nights do night apply. So with above 32, things will start to melt day and night. Dry air coming in will help sublimate things (ie, solid to gas skipping the liquid step) evaporating the snow pack day and night. Lastly, if we do clear, day time radiation will also finish off the pack. Will it be gone in one day? Probably not but it wont linger too far into the week once cleared. And if we do go back into the fog, even worst since fog is a rime/snow killer when above freezing.
So when would be the better day? If you live close enough, try Tuesday since the snow will look crisper and further down but you do run the chance of summit fog tomorrow. Wednesday will have some melt off but looks to remain a better shot at clearing. The best thing to do is go to:
You will enter KMWN as the station for the summit, change the time period to six hours or more and look at raw or decoded details and hit submit. If you see clearing in obs, you will see clearing from the valleys. There are other places you can check our obs, this is just what I used when going to school so I am most familiar with it. The webcams can also be useful, although they do not work well overnight, so not sure how useful they will be. But keep an eye on them as late as visibly possible and judge from there.
Hope this helps as best it can. Sorry I cannot be more definate but at least my prediction of Tuesday is looking OK. Good luck and let us know how you make out.
Staff Meteorologist/Night Observer, KMWN (Mt Washington Obs., NH)